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Martin Schechter


DEGREES

B.S., City University of New York
M.S.,New York University
Ph.D.,New York University


RESEARCH AREA
Partial Differential Equations, Functional Analysis, Critical Point Theory, Operator Theory, Spectral and Scattering Theory, Quantum Mechanics


PROFESSIONAL EXPERIENCE

1957-59              Instructor, N.Y.U.
1959-61              Assistant Professor, N.Y.U.
1961-65              Associate Professor, N.Y.U.
1961                   Visiting Associate Professor, University of Chicago
1965-66              Professor, N.Y.U.
1966-83              Professor, Yeshiva University
1973                   Visiting Professor, Hebrew University
1979                   Visiting Professor, Autonomous University of Mexico
1983-                  Professor, University of California, Irvine


AWARDS AND HONORS

NSF Senior Postdoctoral Fellowship, 1965-66
Member, Institute for Advanced Study, Princeton

MAJOR ADDRESSES

Invited plenary speaker at the Joint U.S. - U.S.S.R. Symposium on Partial Differential Equations, Novosibirsk, 1963, at the invitation of the Soviet Academy of Sciences
Delivered a series of eight lectures as an invited plenary speaker at the Centro Internazionale Matematico Estivo (C.I.M.E.), Varenna, 1973. Lectures published by Edizioni Cremonese, Rome, 1974.
"Variational methods in P.D.E.," A series of four two hour lectures at York University, April 30-May3, 1990.
Invited plenary speaker at the UAB International Conferences on Differential Equations and Mathematical Physics, Birmingham, 1982 - 1988.


PUBLICATIONS

[1] 1 861 991 Schechter, Martin Principles of functional analysis. Second edition. Graduate Studies in Mathematics, 36. American Mathematical Society, Providence, RI, 2002. xxii+425 pp. ISBN: 0-8218-2895-9 46-01 (47-01)

[2] 1 813 000 (Review) Perera, Kanishka; Schechter, Martin Semilinear elliptic equations having asymptotic limits at zero and infinity. Abstr. Appl. Anal. 4 (1999), no. 4, 231--242. (Reviewer: David Arcoya) 35J60 (35J65 58E05)

[3] 2002c:35114 Perera, Kanishka; Schechter, Martin Solution of nonlinear equations having asymptotic limits at zero and infinity. Calc. Var. Partial Differential Equations 12 (2001), no. 4, 359--369. (Reviewer: Fabiana Leoni) 35J65 (35J20)

[4] 2002b:58015 Perera, Kanishka; Schechter, Martin Applications of Morse theory to the solution of semilinear problems depending on $C\sp 1$ functionals. Nonlinear Anal. 45 (2001), no. 1, Ser. A: Theory Methods, 1--9. (Reviewer: Marco Squassina) 58E05 (35J60 35J65)

[5] 2001m:35116 Perera, Kanishka; Schechter, Martin The Fu\v cík spectrum and critical groups. Proc. Amer. Math. Soc. 129 (2001), no. 8, 2301--2308 (electronic). (Reviewer: Xiaofeng Ren) 35J60 (35J20 35J65 49J10 58E05)

[6] 2001k:35100 Perera, Kanishka; Schechter, Martin Multiple nontrivial solutions of elliptic semilinear equations. Topol. Methods Nonlinear Anal. 16 (2000), no. 1, 1--15. (Reviewer: Yong Qing Li) 35J60 (35J20 35J65 58E05)

[7] 2001k:35099 Perera, Kanishka; Schechter, Martin A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities. NoDEA Nonlinear Differential Equations Appl. 7 (2000), no. 4, 361--367. (Reviewer: João Marcos Bezerra do Ó) 35J60 (35J20 35J65 49J20 58E05)

[8] 2001f:58032 Schechter, Martin Linking methods in critical point theory. Birkhäuser Boston, Inc., Boston, MA, 1999. xviii+294 pp. ISBN: 0-8176-4095-9 (Reviewer: Jean-Noël Corvellec) 58E05 (35J65 47J30 58E30)

[9] 2001f:35138 Perera, Kanishka; Schechter, Martin Nontrivial solutions of elliptic semilinear equations at resonance. Manuscripta Math. 101 (2000), no. 3, 301--311. (Reviewer: Gianni Arioli) 35J60 (35D05 58E05)

[10] 2001e:58012 Schechter, Martin Resonance problems with respect to the Fu\v cík spectrum. Trans. Amer. Math. Soc. 352 (2000), no. 9, 4195--4205 (electronic). (Reviewer: Jie Yang) 58E05 (35J65 47J30 49J40)

[11] 2000h:35052 Perera, Kanishka; Schechter, Martin Type II regions between curves of the Fu\v cik spectrum and critical groups. Topol. Methods Nonlinear Anal. 12 (1998), no. 2, 227--243. (Reviewer: Jie Yang) 35J65 (58E05)

[12] 2000e:35156 Schechter, Martin Rotationally invariant periodic solutions of semilinear wave equations. Abstr. Appl. Anal. 3 (1998), no. 1-2, 171--180. (Reviewer: Eduard Feireisl) 35L70 (35B10)

[13] 99j:58043 Perera, Kanishka; Schechter, Martin Morse index estimates in saddle point theorems without a finite-dimensional closed loop. Indiana Univ. Math. J. 47 (1998), no. 3, 1083--1095. (Reviewer: Maria Letizia Bertotti) 58E05 (35J65)

[14] 99h:58035 Schechter, Martin New linking theorems. Rend. Sem. Mat. Univ. Padova 99 (1998), 255--269. (Reviewer: Jean Mawhin) 58E05 (35J65 47H15)

[15] 99h:58034 Schechter, Martin Infinite-dimensional linking. Duke Math. J. 94 (1998), no. 3, 573--595. (Reviewer: Miguel Ramos) 58E05 (35J60 47H15)

[16] 99h:58033 Schechter, Martin Critical point theory with weak-to-weak linking. Comm. Pure Appl. Math. 51 (1998), no. 11-12, 1247--1254. (Reviewer: Miguel Ramos) 58E05 (35J60 47H15)

[17] 99e:35072 Schechter, Martin Eigenvalue problems for semilinear equations. Spectral and scattering theory (Newark, DE, 1997), 157--175, Plenum, New York, 1998. (Reviewer: Wen Xiong Chen) 35J65

[18] 99b:35071 Schechter, Martin Type (II) regions between curves of the Fucik spectrum. NoDEA Nonlinear Differential Equations Appl. 4 (1997), no. 4, 459--476. (Reviewer: Jesús Hernández) 35J65 (47H12 58E05)

[19] 98d:35082 Schechter, Martin Resonance problems which intersect many eigenvalues. Math. Nachr. 183 (1997), 201--210. (Reviewer: Marco Degiovanni) 35J65 (35B99 47H15 58E05)

[20] 97k:35084 Schechter, M.; Tintarev, K. Critical points for pairs of functionals and semilinear elliptic equations. Calculus of variations, applications and computations (Pont-à-Mousson, 1994), 245--253, Pitman Res. Notes Math. Ser., 326, Longman Sci. Tech., Harlow, 1995. (Reviewer: J. V. A. Gonçalves) 35J65 (35B05 49J10)

[21] 97f:58033 Schechter, Martin Critical points when there is no saddle point geometry. Topol. Methods Nonlinear Anal. 6 (1995), no. 2, 295--308. (Reviewer: Jean-Noël Corvellec) 58E05 (35J65 47H15 49K25)

[22] 97a:58033 Schechter, Martin New techniques in critical point theory. Partial differential equations and applications, 289--294, Lecture Notes in Pure and Appl. Math., 177, Dekker, New York, 1996. (Reviewer: Dorin Andrica) 58E05 (47H15)

[23] 97a:58032 Schechter, Martin The intrinsic mountain pass. Pacific J. Math. 171 (1995), no. 2, 529--544. (Reviewer: Jean-Noël Corvellec) 58E05 (35J65 47H15)

[24] 96j:58033 Schechter, Martin The saddle point alternative. Amer. J. Math. 117 (1995), no. 6, 1603--1626. (Reviewer: Miguel Ramos) 58E05 (35J20)

[25] 96h:58029 Berger, Melvyn; Schechter, Martin; Sun, Guo Zhang Infinite-dimensional singularity theory and bifurcation from equilibria for certain nonlinear evolution equations. Topol. Methods Nonlinear Anal. 4 (1994), no. 2, 341--353. (Reviewer: Jesús Hernández) 58E07 (34G20 35B10 35K60 47H15 47N20 58C27)

[26] 96e:35052 Schechter, Martin Superlinear elliptic boundary value problems. Manuscripta Math. 86 (1995), no. 3, 253--265. (Reviewer: Wen Xiong Chen) 35J65 (58E05)

[27] 96c:35063 Schechter, Martin The Fu\v cík spectrum. Indiana Univ. Math. J. 43 (1994), no. 4, 1139--1157. (Reviewer: Yi Hong Du) 35J65 (35P30 47H12 47N20)

[28] 96b:35075 Schechter, Martin Bounded resonance problems for semilinear elliptic equations. Nonlinear Anal. 24 (1995), no. 10, 1471--1482. (Reviewer: Rolando Magnanini) 35J65 (47H12)

[29] 96b:35074 Schechter, Martin Elliptic resonance problems with unequal limits at infinity. Math. Ann. 300 (1994), no. 4, 629--642. (Reviewer: Mario M. Coclite) 35J65 (47H12 47N20 58E05)

[30] 96a:47101 Schechter, Martin The Hampwile alternative. Comm. Appl. Nonlinear Anal. 1 (1994), no. 4, 13--46. (Reviewer: Norman Dancer) 47H12 (35J60 47N20 58E05)

[31] 95k:58033 Schechter, Martin; Tintarev, Kyril Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems. Bull. Soc. Math. Belg. Sér. B 44 (1992), no. 3, 249--261. (Reviewer: Miguel Ramos) 58E05 (35J60)

[32] 95i:35107 Schechter, Martin Strong resonance problems for elliptic semilinear boundary value problems. J. Operator Theory 30 (1993), no. 2, 301--314. (Reviewer: Alexander A. Pankov) 35J65 (35J20 47F05 47H12 58E05)

[33] 95e:58038 Schechter, Martin Splitting subspaces and saddle points. Appl. Anal. 49 (1993), no. 1-2, 33--48. (Reviewer: Miguel Ramos) 58E05 (35J65 49J35)

[34] 95c:35108 Schechter, Martin Asymptotically linear elliptic boundary value problems. Monatsh. Math. 117 (1994), no. 1-2, 121--137. (Reviewer: Xi Ping Zhu) 35J65

[35] 95c:35107 Schechter, Martin Landesman-Lazer resonance problems and saddle point methods. Math. Methods Appl. Sci. 17 (1994), no. 4, 229--238. (Reviewer: Xi Ping Zhu) 35J65 (47H12 47N20)

[36] 94m:58037 Schechter, Martin Semilinear boundary value problems of the strong resonance type. Topol. Methods Nonlinear Anal. 2 (1993), no. 2, 189--202. (Reviewer: J. V. A. Gonçalves) 58E05 (35J65 47H15 47N20 49J27)

[37] 94i:58034 Schechter, Martin New saddle point theorems. Generalized functions and their applications (Varanasi, 1991), 213--219, Plenum, New York, 1993. (Reviewer: Norman Dancer) 58E05 (35J60 47H15 47N20)

[38] 94f:47074 Schechter, M.; Tintarev, K. Nonlinear eigenvalues and mountain pass methods. Topol. Methods Nonlinear Anal. 1 (1993), no. 2, 183--201. (Reviewer: Yi Hong Du) 47H12 (47H15 58E05)

[39] 94e:58022 Schechter, Martin Critical points over splitting subspaces. Nonlinearity 6 (1993), no. 3, 417--427. (Reviewer: Jean Mawhin) 58E05 (35J35 35J50 49Q15)

[40] 94c:58028 Schechter, Martin A generalization of the saddle point method with applications. Ann. Polon. Math. 57 (1992), no. 3, 269--281. (Reviewer: Marco Degiovanni) 58E05 (35J65 47H99 47N20 49J35)

[41] 93c:58045 Schechter, Martin A saddle point theorem applied to semilinear boundary value problems. Panamer. Math. J. 1 (1991), no. 2, 1--25. (Reviewer: Jean Mawhin) 58E05 (35J65 49J35)

[42] 92m:35197 Schechter, Martin; Tintarev, Kyril Families of "first eigenfunctions" for semilinear elliptic eigenvalue problems. Duke Math. J. 62 (1991), no. 2, 453--465. (Reviewer: Claude Do) 35P30 (35J60 47H12 47N20)

[43] 92k:35107 Schechter, Martin A variation of the mountain pass lemma and applications. J. London Math. Soc. (2) 44 (1991), no. 3, 491--502. (Reviewer: William K. Ziemer) 35J65 (35J20)

[44] 92i:47076 Schechter, Martin; Tintarev, Kyril Points of spherical maxima and solvability of semilinear elliptic equations. Canad. J. Math. 43 (1991), no. 4, 825--831. (Reviewer: Yi Hong Du) 47H12 (35J65 35P30 47H15 47N20)

[45] 92h:58040 Schechter, Martin A bounded mountain pass lemma without the (PS) condition and applications. Trans. Amer. Math. Soc. 331 (1992), no. 2, 681--703. (Reviewer: Jean Mawhin) 58E05 (35J60 47H99 49J52 58E50)

[46] 92h:58039 Schechter, Martin The mountain cliff theorem. Differential equations and mathematical physics (Birmingham, AL, 1990), 263--279, Math. Sci. Engrg., 186, Academic Press, Boston, MA, 1992. (Reviewer: Jean Mawhin) 58E05 (35J65)

[47] 92d:58033 Schechter, Martin The mountain pass alternative. Adv. in Appl. Math. 12 (1991), no. 1, 91--105. (Reviewer: Norman Dancer) 58E05 (35J50 47H15)

[48] 92c:47077 Schechter, Martin; Tintarev, Kyril Eigenvalues for semilinear boundary value problems. Arch. Rational Mech. Anal. 113 (1990), no. 3, 197--208. (Reviewer: Ricardo S. Kubrusly) 47H15 (35J65 35P30)

[49] 92b:35063 Schechter, Martin Nonlinear elliptic boundary value problems at resonance. Nonlinear Anal. 14 (1990), no. 10, 889--903. (Reviewer: R. Kent Nagle) 35J65 (47H15 58G20)

[50] 92b:35057 Schechter, Martin Solution of nonlinear problems at resonance. Indiana Univ. Math. J. 39 (1990), no. 4, 1061--1080. (Reviewer: Paolo Acquistapace) 35J60 (35J35 47H15)

[51] 91m:35094 Schechter, Martin Nonlinear elliptic boundary value problems at strong resonance. Amer. J. Math. 112 (1990), no. 3, 439--460. (Reviewer: R. Kent Nagle) 35J65 (47H15 58E05)

[52] 91i:35081 Schechter, Martin; Tintarev, Kyril Spherical maxima in Hilbert space and semilinear elliptic eigenvalue problems. Differential Integral Equations 3 (1990), no. 5, 889--899. (Reviewer: Zuchi Chen) 35J65 (35P30 47H12 47H15)

[53] 91g:35145 Berger, M. S.; Schechter, M. Bifurcation from equilibria for certain infinite-dimensional dynamical systems. Mathematics of nonlinear science (Phoenix, AZ, 1989), 133--138, Contemp. Math., 108, Amer. Math. Soc., Providence, RI, 1990. (Reviewer: Jesús Hernández) 35K60 (35B32 35Q72 58E07)

[54] 90j:47080 Schechter, Martin The Hampwile theorem for nonlinear eigenvalues. Duke Math. J. 59 (1989), no. 2, 325--335. (Reviewer: E. Tarafdar) 47H12 (47H15 58E05)

[55] 90i:42031 Schechter, Martin Multiplication operators. Canad. J. Math. 41 (1989), no. 2, 234--249. (Reviewer: Ron Kerman) 42B25 (47A30 47B38)

[56] 90g:35059 Schechter, Martin Boundary value problems for semilinear elliptic equations of arbitrary order in unbounded domains. Rocky Mountain J. Math. 18 (1988), no. 3, 519--534. (Reviewer: D. E. Edmunds) 35J65

[57] 89m:26029 Schechter, Martin Exact estimates for potentials. SIAM J. Math. Anal. 19 (1988), no. 6, 1324--1328. (Reviewer: Yoshimi Sait\=o) 26D10

[58] 89k:47019 Schechter, M.; Whitley, Robert Best Fredholm perturbation theorems. Studia Math. 90 (1988), no. 3, 175--190. (Reviewer: Jaroslav Zemánek) 47A53 (47A55)

[59] 89k:35169 Schechter, Martin The spectrum of the Schrödinger operator. Trans. Amer. Math. Soc. 312 (1989), no. 1, 115--128. (Reviewer: Hitoshi Kitada) 35P15 (26D10 35J10 47F05)

[60] 89k:26010 Schechter, Martin Weighted norm inequalities for potential operators. Trans. Amer. Math. Soc. 308 (1988), no. 1, 57--68. (Reviewer: L. Losonczi) 26D10 (42B25 47A30)

[61] 89g:46068 Schechter, Martin Potential estimates in Orlicz spaces. Pacific J. Math. 133 (1988), no. 2, 381--399. (Reviewer: Bruno Franchi) 46E35 (26D15 35G30)

[62] 88k:46036 Schechter, Martin Weighted norm estimates for Sobolev spaces. Trans. Amer. Math. Soc. 304 (1987), no. 2, 669--687. (Reviewer: Yu. A. Brudny\u\i) 46E35 (26D20)

[63] 88h:35085 Schechter, Martin Spectra of partial differential operators. Second edition. North-Holland Series in Applied Mathematics and Mechanics, 14. North-Holland Publishing Co., Amsterdam, 1986. xiv+310 pp. ISBN: 0-444-87822-X (Reviewer: A. Devinatz) 35Pxx (47F05)

[64] 88f:35120 Schechter, Martin Two space scattering and propagative systems. Illinois J. Math. 31 (1987), no. 1, 62--88. (Reviewer: J. Weidmann) 35P25 (47A40 47F05)

[65] 88e:35079 Schechter, Martin Semilinear boundary value problems for unbounded domains. Michigan Math. J. 34 (1987), no. 1, 63--76. (Reviewer: J. Ka\v cur) 35J65 (35J35)

[66] 87d:49030 Schechter, Martin Derivatives of mappings with applications to nonlinear differential equations. Trans. Amer. Math. Soc. 293 (1986), no. 1, 53--69. (Reviewer: Péter Tallós) 49A52 (46G05)

[67] 87a:47031 Schechter, Martin Selfadjoint operators, spectral and scattering theory, variational techniques, nonlinear phenomena, linear and nonlinear partial differential equations, and related topics. Differential equations (Birmingham, Ala., 1983), 501--509, North-Holland Math. Stud., 92, North-Holland, Amsterdam, 1984. 47Bxx (35R20 47Axx 47Hxx 58G99)

[68] 86g:46062 Schechter, Martin Differentiation in abstract spaces. J. Differential Equations 55 (1984), no. 3, 330--345. (Reviewer: A. B. Németh) 46G05 (58C20)

[69] 85m:47007 Schechter, Martin Selfadjoint realizations in another Hilbert space. Amer. J. Math. 106 (1984), no. 1, 43--65. (Reviewer: J. Weidmann) 47A55 (47A40 47B25)

[70] 85g:46042 Schechter, Martin Imbedding estimates involving new norms and applications. Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 163--166. (Reviewer: J. S. Martins) 46E35 (47B38)

[71] 83h:81055 Schechter, Martin; Weder, R. A. Dyons exist. Contributions to analysis and geometry (Baltimore, Md., 1980), pp. 311--319, Johns Hopkins Univ. Press, Baltimore, Md., 1981. 81E10 (58C20 81G10)

[72] 83b:81004 Schechter, Martin Operator methods in quantum mechanics. North-Holland Publishing Co., New York-Amsterdam, 1981. xx+324 pp. ISBN: 0-444-00410-6 (Reviewer: Lawrence E. Thomas) 81-01 (35Pxx 47Axx 47Bxx 81C10 81Fxx)

[73] 83b:35031 Schechter, M.; Simon, B. Unique continuation for Schrödinger operators with unbounded potentials. J. Math. Anal. Appl. 77 (1980), no. 2, 482--492. 35J10 (81F05)

[74] 83a:47011 Schechter, Martin Wave operators for pairs of spaces and the Klein-Gordon equation. Aequationes Math. 20 (1980), no. 1, 38--50. (Reviewer: H. Baumgärtel) 47A40 (35P25 81F05)

[75] 82h:81095 Schechter, M.; Weder, R. A theorem on the existence of dyon solutions. Ann. Physics 132 (1981), no. 2, 292--327. (Reviewer: José M. Cerveró) 81E10 (58E30)

[76] 82c:35001 Bers, Lipman; John, Fritz; Schechter, Martin Partial differential equations. With supplements by Lars G\.arding and A. N. Milgram. With a preface by A. S. Householder. Reprint of the 1964 original. Lectures in Applied Mathematics, 3{\rm A}. American Mathematical Society, Providence, R.I., 1979. xiii+343 pp. ISBN: 0-8218-0049-3 35-02

[77] 81k:47014 Schechter, Martin The continuous singular spectrum of the Schrödinger operator. Math. Proc. Cambridge Philos. Soc. 88 (1980), no. 1, 59--69. (Reviewer: W. Allegretto) 47A40 (35P05 81C10)

[78] 81g:81058 Schechter, Martin; Weder, Ricardo Rigorous results on the existence of dyon solutions. Phys. Rev. Lett. 44 (1980), no. 20, 1303--1305. 81E10 (58E20)

[79] 81g:47069 Schechter, Martin; Shapiro, Jack; Snow, Morris Solution of the nonlinear problem $Au=N(u)$ in a Banach space. Trans. Amer. Math. Soc. 241 (1978), 69--78. 47H15 (47H10)

[80] 81g:47008 Schechter, Martin Two space scattering theory using the subspace of continuity. Lett. Math. Phys. 3 (1979), no. 6, 521--531. (Reviewer: T. Kato) 47A40 (47A55)

[81] 80i:47012 Schechter, Martin Completeness of wave operators in two Hilbert spaces. Ann. Inst. H. Poincaré Sect. A (N.S.) 30 (1979), no. 2, 109--127. (Reviewer: P. A. Mishnaevski\u \i) 47A40

[82] 80h:47012 Schechter, Martin Scattering in two Hilbert spaces. J. London Math. Soc. (2) 19 (1979), no. 1, 175--186. (Reviewer: M. Demuth) 47A40 (35P25)

[83] 80c:47013 Schechter, Martin The invariance principle. Comment. Math. Helv. 54 (1979), no. 1, 111--125. (Reviewer: M. M. Skriganov) 47A40 (35P25)

[84] 80c:47012 Schechter, Martin Another look at scattering theory. Internat. J. Theoret. Phys. 17 (1978), no. 1, 33--41. (Reviewer: M. M. Skriganov) 47A40

[85] 80c:35078 Schechter, Martin Scattering theory for the Schrödinger operator with potentials not of short range. Complex analysis and its applications (Russian), pp. 601--607, 672, "Nauka", Moscow, 1978. (Reviewer: M. M. Skriganov) 35P25 (47A40)

[86] 58 #23156 Schechter, Martin Essential self-adjointness of the Schrödinger operator with magnetic vector potential. J. Functional Analysis 20 (1975), no. 2, 93--104. 35P05

[87] 58 #17997 Berger, Melvyn S.; Schechter, Martin On the solvability of semilinear gradient operator equations. Advances in Math. 25 (1977), no. 2, 97--132. (Reviewer: R. Kannan) 47H15 (58E99)

[88] 58 #17586 Koller, Herbert; Schechter, Martin; Weder, Ricardo A. Schrödinger operators in the uniform norm. Ann. Inst. H. Poincaré Sect. A (N.S.) 26 (1977), no. 3, 303--311. (Reviewer: Richard B. Lavine) 35P05 (35J10)

[89] 58 #17436 Schechter, Martin Modern methods in partial differential equations. An introduction. McGraw-Hill International Book Co., New York-Bogotá-Auckland, 1977. xiv+245 pp. ISBN: 0-07-055193-6 (Reviewer: Ju. V. Kostarcuk) 35-01

[90] 58 #11884 Freeman, R. S.; Schechter, Martin On the existence, uniqueness and regularity of solutions to general elliptic boundary-value problems. J. Differential Equations 15 (1974), 213--246. (Reviewer: Melvin Heard) 35J40

[91] 58 #7140 Schechter, Martin A new criterion for scattering theory. Duke Math. J. 44 (1977), no. 4, 863--872. (Reviewer: Richard B. Lavine) 47A40 (35P25 81.47)

[92] 57 #17027 Schechter, Martin Discreteness of the singular spectrum for Schrödinger operators. Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 1, 121--133. 35P25 (47A40)

[93] 57 #10275 Schechter, Martin Nonhomogeneous elliptic systems and scattering. Tôhoku Math. J. (2) 27 (1975), no. 4, 601--616. 35P25 (35J45 47A40)

[94] 57 #8629 Schechter, Martin Wave operators for oscillating potentials. Lett. Math. Phys. 2 (1977/78), no. 2, 127--132. (Reviewer: Woodford W. Zachary) 81.35

[95] 57 #7085 Schechter, Martin Principles of functional analysis. Student edition. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. xix+383 pp. 46-01 (47-01)

[96] 57 #6887 Schechter, M.; Weder, R. The Schrödinger operator with vector potential. Comm. Partial Differential Equations 2 (1977), no. 5, 549--561. (Reviewer: C. A. Swanson) 35P05

[97] 57 #917 Schechter, Martin The Klein-Gordon equation and scattering theory. Ann. Physics 101 (1976), no. 2, 601--609. (Reviewer: Teruo Ikebe) 35P25

[98] 57 #914 Schechter, Martin Scattering theory for elliptic systems. J. Math. Soc. Japan 28 (1976), no. 1, 71--79. (Reviewer: J. Thomas Beale) 35P20

[99] 56 #12969 Schechter, Martin Cut-off potentials and forms extensions. Lett. Math. Phys. 1 (1975/77), no. 4, 265--273. (Reviewer: Derek W. Robinson) 47B37

[100] 56 #6144 Schechter, Martin Spectra of partial differential operators. North-Holland Series in Applied Mathematics and Mechanics, Vol. 14. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1971. xiii+268 pp. 35P05

[101] 56 #3607 Schechter, Martin Principles of functional analysis. Academic Press, New York-London, 1971. xix+383 pp. 46-01 (47-01)

[102] 55 #13097 Schechter, Martin Eigenfunction expansions for the Schrödinger operator. Ark. Mat. 14 (1976), no. 2, 277--287. (Reviewer: M. M. Skriganov) 35P10 (35J10)

[103] 55 #11075 Schechter, Martin The existence of wave operators in scattering theory. Bull. Amer. Math. Soc. 83 (1977), no. 3, 381--383. (Reviewer: Boris Pavlov) 47A40 (35P25)

[104] 55 #8851 Schechter, Martin Remarks on a previous paper: "On the essential spectrum of an arbitrary operator. I", (J. Math. Anal. Appl. 13 (1966), 205--215). J. Math. Anal. Appl. 54 (1976), no. 1, 138--141. (Reviewer: T. Kato) 47B30 (47A55)

[105] 55 #3524 Schechter, Martin Differentiability of solutions of elliptic problems with respect to parameters. Boll. Un. Mat. Ital. A (5) 13 (1976), no. 3, 601--608. (Reviewer: V. A. Kondratev) 35J30

[106] 53 #14230 Schechter, Martin Scattering theory for pseudodifferential operators. Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 111--121. (Reviewer: F. Cardoso) 47G05 (35P25 47A40)

[107] 53 #13869 Schechter, Martin Scattering theory for second order elliptic operators. Ann. Mat. Pura Appl. (4) 105 (1975), 313--331. (Reviewer: T. Kato) 35P25 (47A40)

[108] 53 #13865 Schechter, Martin On the spectra of singular elliptic operators. Mathematika 23 (1976), no. 1, 107--115. (Reviewer: J. R. Kuttler) 35P15

[109] 52 #14684 Spectral analysis. Centro Internazionale Matematico Estivo (C.I.M.E.), III Ciclo, Varenna, 24 Agosto--2 Settembre 1973. Coordinatore: J. Cecconi. Edizioni Cremonese, Rome, 1974. ii+253 pp. 35PXX (47-06)

[110] 51 #13728 Schechter, M.; Snow, M. The Fredholm spectrum on tensor products. Proc. Roy. Irish Acad. Sect. A 75 (1975), no. 13, 121--127. (Reviewer: Robin Harte) 47A10

[111] 51 #6450 Schechter, Martin Proper boundary points of the spectrum. Osaka J. Math. 12 (1975), 41--44. (Reviewer: C. R. Putnam) 47A10

[112] 51 #6141 Schechter, Martin A nonlinear elliptic boundary value problem. Ann. Scuola Norm. Sup. Pisa (3) 27 (1973), 707--716 (1974). (Reviewer: J. E. Lagnese) 35J65

[113] 51 #3726 Schechter, Martin Scattering theory for elliptic operators of arbitrary order. Comment. Math. Helv. 49 (1974), 84--113. (Reviewer: C. Bardos) 35P25

[114] 51 #1436 Schechter, Martin A unified approach to scattering. J. Math. Pures Appl. (9) 53 (1974), 373--396. (Reviewer: T. Kato) 47A40 (35P25)

[115] 48 #7017 Schechter, Martin On the essential spectrum of partial differential operators bounded from below. Scripta Math. 29, 5--16. (1973). (Reviewer: Y. I. Kannai) 47F05

[116] 48 #4773 Schechter, Martin Operators obeying Weyl's theorem. Scripta Math. 29, 67--75. (1973). (Reviewer: K. K. Oberai) 47A10

[117] 47 #2406 Shapiro, Jack; Schechter, Martin A generalized operational calculus developed from Fredholm operator theory. Trans. Amer. Math. Soc. 175 (1973), 439--467. (Reviewer: F. Gilfeather) 47A60 (47B30)

[118] 47 #803 Berger, Melvyn S.; Schechter, Martin Embedding theorems and quasi-linear elliptic boundary value problems for unbounded domains. Trans. Amer. Math. Soc. 172 (1972), 261--278. (Reviewer: A. Kufner) 46E35 (35J65 35L60 49F99)

[119] 46 #4280 Schechter, Martin Hamiltonians for singular potentials. Indiana Univ. Math. J. 22 (1972/73), 483--503. (Reviewer: B. Hellwig) 47F05 (35P99)

[120] 46 #2511 Berger, Melvyn S.; Schechter, Martin On the solvability of semilinear operator equations and elliptic boundary value problems. Bull. Amer. Math. Soc. 78 (1972), 741--745. (Reviewer: J. W. Thomas) 47H15 (35K60)

[121] 45 #4171 Schechter, Martin Quantities related to strictly singular operators. Indiana Univ. Math. J. 21 (1971/72), 1061--1071. (Reviewer: J. D. Gray) 47B99

[122] 42 #8301 Lebow, Arnold; Schechter, Martin Semigroups of operators and measures of noncompactness. J. Functional Analysis 7 1971 1--26. (Reviewer: J. D. Gray) 46.65 (47.00)

[123] 42 #2325 Schechter, Martin The spectrum of operators on $L\sp{p}\,(E\sp{n})$. Ann. Scuola Norm. Sup. Pisa (3) 24 1970 201--207. (Reviewer: Y. I. Kannai) 47.65 (35.00)

[124] 42 #2294 Berger, Melvyn S.; Schechter, Martin $L\sb{p}$ embedding and nonlinear eigenvalue problems for unbounded domains. Bull. Amer. Math. Soc. 76 1970 1299--1302. (Reviewer: S. Newberger) 46.38 (35.00)

[125] 41 #5992 Dash, A. T.; Schechter, M. Tensor products and joint spectra. Israel J. Math. 8 1970 191--193. (Reviewer: C. Pearcy) 47.30

[126] 41 #4273 Schechter, Martin The conjugate of a product of operators. J. Functional Analysis 6 1970 26--28. (Reviewer: S. S. Holland, Jr.) 47.10

[127] 41 #2431 Schechter, Martin On the spectra of operators on tensor products. J. Functional Analysis 4 1969 95--99. (Reviewer: A. Brown) 47.30

[128] 40 #7876 Schechter, Martin Partial differential operators on $L\sp{p}\,(E\sp{n})$. Bull. Amer. Math. Soc. 75 1969 548--549. (Reviewer: P. Grisvard) 47.65 (35.00)

[129] 40 #6091 Schechter, M. The spectra of non-elliptic operators. Israel J. Math. 6 1968 384--397 (1969). (Reviewer: F. H. Brownell) 35.80 (47.00)

[130] 40 #3348 Lebow, Arnold; Schechter, Martin Norms on quotient spaces. Bull. Amer. Math. Soc. 75 1969 1322--1325. (Reviewer: S. Goldberg) 47.40

[131] 40 #1809 Schechter, Martin On perturbations of essential spectra. J. London Math. Soc. (2) 1 1969 343--347. (Reviewer: K. Gustafson) 47.48

[132] 40 #579 Schechter, Martin On the essential spectrum of an elliptic operator perturbed by a potential. J. Analyse Math. 22 1969 87--115. (Reviewer: J. Smoller) 35.80 (47.00)

[133] 38 #565 Schechter, Martin On the invariance of the essential spectrum of an arbitrary operator. III. Proc. Cambridge Philos. Soc. 64 1968 975--984. (Reviewer: C. Clark) 47.30

[134] 37 #6777 Schechter, Martin Riesz operators and Fredholm perturbations. Bull. Amer. Math. Soc. 74 1968 1139--1144. (Reviewer: S. R. Caradus) 47.10

[135] 37 #5718 Schechter, Martin On the invariance of the essential spectrum of an arbitrary operator. II. Ricerche Mat. 16 1967 3--26. (Reviewer: C. Clark) 47.30

[136] 37 #3364 Coburn, L. A.; Schechter, Martin Joint spectra and interpolation of operators. J. Functional Analysis 2 1968 226--237. (Reviewer: M. Cotlar) 46.65 (47.00)

[137] 36 #6977 Schechter, Martin Basic theory of Fredholm operators. Ann. Scuola Norm. Sup. Pisa (3) 21 1967 261--280. (Reviewer: S. Goldberg) 47.45

[138] 36 #6927 Schechter, Martin Complex interpolation. Compositio Math. 18 1967 117--147 (1967). (Reviewer: J. Peetre) 46.38

[139] 36 #2016 Schechter, Martin Intermediate extensions in $L\sp{p}$. Bull. Amer. Math. Soc. 73 1967 979--985. (Reviewer: T. Kato) 47.65 (35.00)

[140] 35 #3486 Schechter, Martin Essential spectra of elliptic partial differential equations. Bull. Amer. Math. Soc. 73 1967 567--572. (Reviewer: C. Clark) 47.65

[141] 34 #7931 Bers, L.; D\v zon, F.; \v Sehter, M. {\cyr Uravneniya s chastnymi proizvodnymi}. (Russian) [Partial differential equations] With special lectures by Lars Garding and A. N. Milgram. Translated from the English by Ju. V. Egorov. Edited by O.A. Ole\u\i nik Izdat. ``Mir'', Moscow 1966 351 pp. 35.00

[142] 33 #6146 Schechter, Martin Nonlocal elliptic boundary value problems. Ann. Scuola Norm. Sup. Pisa (3) 20 1966 421--441. (Reviewer: Colin Clark) 35.45

[143] 33 #6094 Schechter, Martin On the theory of differential boundary problems. Illinois J. Math. 7 1963 232--245. (Reviewer: R. S. Freeman) 35.31

[144] 33 #558 Schechter, Martin Interpolation spaces by complex methods. Bull. Amer. Math. Soc. 72 1966 526--533. (Reviewer: I. G. Amemiya) 46.38 (46.10)

[145] 32 #6230 Schechter, Martin On the essential spectrum of an arbitrary operator. I. J. Math. Anal. Appl. 13 1966 205--215. (Reviewer: T. Kato) 47.10

[146] 32 #6052 Schechter, Martin On $L\sp{p}$ estimates and regularity. II. Math. Scand. 13 1963 47--69. (Reviewer: R. Beals) 35.19

[147] 32 #6051 Schechter, Martin On $L\sp{p}$ estimates and regularity. I. Amer. J. Math. 85 1963 1--13. (Reviewer: R. Beals) 35.19

[148] 32 #6050 Schechter, Martin On the dominance of partial differential operators. II. Ann. Scuola Norm. Sup. Pisa (3) 18 1964 255--282. (Reviewer: R. Carroll) 35.39

[149] 32 #6049 Schechter, Martin On the dominance of partial differential operators. Trans. Amer. Math. Soc. 107 1963 i37--260. (Reviewer: R. Carroll) 35.39

[150] 31 #3713 Schechter, Martin On $L\sp{p}$ estimates and regularity. III. Ricerche Mat. 13 1964 192--206. (Reviewer: J. Peetre) 35.24

[151] 31 #3710 Ercolano, Joseph; Schechter, Martin Spectral theory for operators generated by elliptic boundary problems with eigenvalue parameter in boundary conditions. II. Comm. Pure Appl. Math. 18 1965 397--414. (Reviewer: J. Peetre) 35.80 (47.65)

[152] 31 #1576 Ercolano, Joseph; Schechter, Martin Spectral theory for operators generated by elliptic boundary problems with eigenvalue parameter in boundary conditions. I. Comm. Pure Appl. Math. 18 1965 83--105. (Reviewer: J. Peetre) 47.65 (35.80)

[153] 30 #5167 Schechter, Martin Invariance of the essential spectrum. Bull. Amer. Math. Soc. 71 1965 365--367. (Reviewer: T. Kato) 47.10 (47.48)

[154] 30 #1303b Schechter, Martin General boundary value problems for elliptic partial differential equations. Bull. Amer. Math. Soc. 65 1959 70--72. (Reviewer: L. Carding) 35.45

[155] 30 #1303a Schechter, Martin Solution of the Dirichlet problem for equations not necessarily strongly elliptic. Bull. Amer. Math. Soc. 64 1958 371--372. 35.45

[156] 30 #1302 Schechter, Martin Observations concerning a paper of Peetre. Comm. Pure Appl. Math. 14 1961 733--736. (Reviewer: C. Racine) 35.45 (46.40)

[157] 29 #6181 Schechter, Martin Systems of partial differential equations in a half-space. Comm. Pure Appl. Math. 17 1964 423--434. (Reviewer: J. Peetre) 35.39

[158] 29 #2513 Bers, Lipman; Schechter, Martin Elliptic equations. 1964 Partial Differential Equations (Proc. Summer Seminar, Boulder, Col., 1957) pp. 131--299 Interscience, New York (Reviewer: R. Carroll) 35.00 (35.42)

[159] 29 #346 Bers, Lipman; John, Fritz; Schechter, Martin Partial differential equations. With special lectures by Lars Garding and A. N. Milgram. Proceedings of the Summer Seminar, Boulder, Colorado, 1957. Lectures in Applied Mathematics, Vol. III Interscience Publishers John Wiley & Sons, Inc.\,New York-London-Sydn ey 1957 xiii+343 pp. 35.00

[160] 28 #1381 Schechter, Martin A local regularity theorem. J. Math. Mech. 10 1961 279--287. (Reviewer: W. F. Donoghue, Jr.) 35.45

[161] 27 #5030 Schechter, Martin Solution of the Dirichlet problem for systems not necessarily strongly elliptic. Comm. Pure Appl. Math. 12 1959 241--247. (Reviewer: J. Peetre) 35.46

[162] 27 #4099 Kaniel, Shmuel; Schechter, Martin Spectral theory for Fredholm operators. Comm. Pure Appl. Math. 16 1963 423--448. (Reviewer: A. E. Taylor) 47.10

[163] 26 #4210 Schechter, Martin Coerciveness in $L\sp{p}$. Trans. Amer. Math. Soc. 107 1963 10--29. (Reviewer: J. Horváth) 47.65 (35.99)

[164] 26 #4032 Schechter, Martin Some unusual boundary value problems. 1961 Proc. Sympos. Pure Math., Vol. IV pp. 109--113 American Mathematical Society, Providence, R.I. (Reviewer: E. Magenes) 35.99

[165] 25 #5276 Schechter, Martin Integral inequalities for partial differential operators and functions satisfying general boundary conditions. Comm. Pure Appl. Math. 12 1959 37--66. (Reviewer: Author's abstract) 35.19

[166] 25 #3281 Schechter, Martin Some $L\sp{p}$ estimates for partial differential equations. Bull. Amer. Math. Soc. 68 1962 470--474. (Reviewer: R. P. Gilbert) 35.19

[167] 24 #A2747 Schechter, Martin Coerciveness of linear partial differential operators for functions satisfying zero Dirichlet-type boundary data. Comm. Pure Appl. Math. 11 1958 153--174. (Reviewer: S. Mizohata) 35.31

[168] 24 #A2139 Schechter, Martin A general approach to boundary problems. Bull. Amer. Math. Soc. 66 1960 495--500. (Reviewer: L. Nachbin) 35.45 (35.31)

[169] 24 #A917 Schechter, Martin A generalization of the problem of transmission. Ann. Scuola Norm. Sup. Pisa (3) 14 1960 207--236. (Reviewer: J. L. Lions) 35.45

[170] 23 #A2636 Schechter, Martin Negative norms and boundary problems. Ann. of Math. (2) 72 1960 581--593. (Reviewer: E. Magenes) 35.45

[171] 23 #A2635 Schechter, Martin Various types of boundary conditions for elliptic equations. Comm. Pure Appl. Math. 13 1960 407--425. (Reviewer: E. Magenes) 35.45

[172] 23 #A2634 Schechter, Martin Mixed boundary problems for general elliptic equations. Comm. Pure Appl. Math. 13 1960 183--201. (Reviewer: E. Magenes) 35.45

[173] 23 #A2633 Schechter, Martin Remarks on elliptic boundary value problems. Comm. Pure Appl. Math. 12 1959 561--578. (Reviewer: E. Magenes) 35.45

[174] 23 #A2626 Schechter, Martin General boundary value problems for elliptic partial differential equations. Comm. Pure Appl. Math. 12 1959 457--486. (Reviewer: G. Bergendal) 35.45

[175] 22 #3872 Schechter, Martin On the Dirichlet problem for second order elliptic equations with coefficients singular at the boundary. Comm. Pure Appl. Math. 13 1960 321--328. (Reviewer: O. A. Ole\u\i nik) 35.00

[176] 22 #2793 Schechter, Martin Elliptic problems in which the boundary conditions do not form a normal set. Bull. Amer. Math. Soc. 66 1960 84--85. (Reviewer: K. T. Smith) 35.00

[177] 22 #2787 Schechter, Martin A free boundary problem for pseudo-analytic functions. Proc. Amer. Math. Soc. 10 1959 881--887. (Reviewer: M. H. Protter) 35.00 (30.00)

[178] 21 #3660 Schechter, Martin General boundary value problems for elliptic partial differential equations. Bull. Amer. Math. Soc. 65 1959 70--72. (Reviewer: K. T. Smith) 35.00

[179] 19,555b Schechter, Martin On estimating elliptic partial differential operators in the $L\sb 2$ norm. Amer. J. Math. 79 (1957), 431--443. (Reviewer: K. T. Smith) 35.0X

[180] 1 819 731 Schechter, Martin Periodic solutions of semilinear higher dimensional wave equations. Chaos Solitons Fractals 12 (2001), no. 6, 1029--1034. 35L70 (35B10)


OTHER PROFESSIONAL ACTIVITIES

MEMBER OF EDITORIAL BOARDS

Communications in Partial Differential Equations, 1973 - 1996
Pan American Mathematical Journal, 1991 - present
Communications on Applied Nonlinear Analysis, 1994 - present
Abstract and Applied Analysis, 1995 - present
International Journal of Differential Equations and Applications, 1998 - present


Ph.D. STUDENTS

Richard Ford

Caryl Margulies

Gianpaolo Evangelista (committee)

Ian Schindler (committee)

Victor Acosta (committee)

Kuo-Tong Thau (committee)

Joseph Mingerone (committee)

Mohammed Sorouri (committee)

William Burns (committee)

Philippe Relouzat


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