Vita
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
- 1 807 945 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.
35J60 (35J20 35J65 49J20 58E05)
- 1 805 036 Perera, Kanishka; Schechter, Martin Multiple nontrivial
solutions of elliptic semilinear equations. Topol. Methods Nonlinear Anal.
16 (2000), no. 1, 1--15. 35J60 (35J20 35J65 58Exx)
- 1 729 208 (Review) Schechter, Martin Linking methods in critical
point
theory. BirkhSuser Boston, Inc., Boston, MA, 1999. xviii+294 pp. ISBN:
0-8176-4095-9 (Reviewer: Jean-NoÔl Corvellec) 58E05 (35J65 47J30 58E30)
- 1 751 035 (Review) 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)
- 1 766 536 (Review) Schechter, Martin Resonance problems with
respect to
the Fu\v cÕk spectrum. Trans. Amer. Math. Soc. 352 (2000), no. 9,
4195--4205
(electronic). (Reviewer: Jie Yang) 58E05 (35J65 47J30 49J40)
- 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)
- 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)
- 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)
- 99h:58035 Schechter, Martin New linking theorems. Rend. Sem. Mat.
Univ.
Padova 99 (1998), 255--269. (Reviewer: Jean Mawhin) 58E05 (35J65 47H15)
- 99h:58034 Schechter, Martin Infinite-dimensional linking. Duke
Math. J.
94 (1998), no. 3, 573--595. (Reviewer: Miguel Ramos) 58E05 (35J60 47H15)
- 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)
- 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
- 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: JesĪs Hernāndez) 35J65 (47H12 58E05)
- 98d:35082 Schechter, Martin Resonance problems which intersect
many eigenvalues. Math. Nachr. 183
(1997), 201--210. (Reviewer: Marco Degiovanni) 35J65 (35B99 47H15 58E05)
- 97k:35084 Schechter, M.; Tintarev, K. Critical points for pairs
of functionals and semilinear elliptic
equations. Calculus of variations, applications and computations
(Pont-ö-Mousson, 1994), 245--253, Pitman Res. Notes
Math. Ser., 326, Longman Sci. Tech., Harlow, 1995. (Reviewer: J. V. A.
Gon?alves) 35J65 (35B05 49J10)
- 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-NoÔl Corvellec)
58E05 (35J65 47H15 49K25)
- 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)
- 97a:58032 Schechter, Martin The intrinsic mountain pass.
Pacific J. Math. 171 (1995), no. 2,
529--544. (Reviewer: Jean-NoÔl Corvellec) 58E05 (35J65 47H15)
- 96j:58033 Schechter, Martin The saddle point alternative.
Amer. J. Math. 117 (1995), no. 6,
1603--1626. (Reviewer: Miguel Ramos) 58E05 (35J20)
- 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: JesĪs Hernāndez) 58E07 (34G20 35B10 35K60
47H15 47N20 58C27)
- 96e:35052 Schechter, Martin Superlinear elliptic boundary
value problems. Manuscripta Math. 86
(1995), no. 3, 253--265. (Reviewer: Wen Xiong Chen) 35J65 (58E05)
- 96c:35063 Schechter, Martin The Fu\v cÕk spectrum. Indiana
Univ. Math. J. 43 (1994), no. 4,
1139--1157. (Reviewer: Yi Hong Du) 35J65 (35P30 47H12 47N20)
- 96b:35075 Schechter, Martin Bounded resonance problems for
semilinear elliptic equations. Nonlinear
Anal. 24 (1995), no. 10, 1471--1482. (Reviewer: Rolando Magnanini) 35J65
(47H12)
- 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)
- 96a:47101 Schechter, Martin The Hampwile alternative. Comm.
Appl. Nonlinear Anal. 1 (1994), no.
4, 13--46. (Reviewer: Norman Dancer) 47H12 (35J60 47N20 58E05)
- 95k:58033 Schechter, Martin; Tintarev, Kyril Pairs of critical
points produced by linking subsets with
applications to semilinear elliptic problems. Bull. Soc. Math. Belg. SZ.
B 44 (1992), no. 3, 249--261. (Reviewer:
Miguel Ramos) 58E05 (35J60)
- 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)
- 95e:58038 Schechter, Martin Splitting subspaces and saddle
points. Appl. Anal. 49 (1993), no. 1-2,
33--48. (Reviewer: Miguel Ramos) 58E05 (35J65 49J35)
- 95c:35108 Schechter, Martin Asymptotically linear elliptic
boundary value problems. Monatsh. Math.
117 (1994), no. 1-2, 121--137. (Reviewer: Xi Ping Zhu) 35J65
- 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)
- 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. Gon?alves) 58E05 (35J65 47H15
47N20 49J27)
- 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)
- 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)
- 94e:58022 Schechter, Martin Critical points over splitting
subspaces. Nonlinearity 6 (1993), no. 3,
417--427. (Reviewer: Jean Mawhin) 58E05 (35J35 35J50 49Q15)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 92d:58033 Schechter, Martin The mountain pass alternative.
Adv. in Appl. Math. 12 (1991), no. 1,
91--105. (Reviewer: Norman Dancer) 58E05 (35J50 47H15)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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: JesĪs Hernāndez) 35K60 (35B32
35Q72 58E07)
- 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)
- 90i:42031 Schechter, Martin Multiplication operators. Canad.
J. Math. 41 (1989), no. 2, 234--249.
(Reviewer: Ron Kerman) 42B25 (47A30 47B38)
- 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
- 89m:26029 Schechter, Martin Exact estimates for potentials.
SIAM J. Math. Anal. 19 (1988), no. 6,
1324--1328. (Reviewer: Yoshimi Sait\=o) 26D10
- 89k:47019 Schechter, M.; Whitley, Robert Best Fredholm
perturbation theorems. Studia Math. 90
(1988), no. 3, 175--190. (Reviewer: Jaroslav Zemānek) 47A53 (47A55)
- 89k:35169 Schechter, Martin The spectrum of the Schrsinger
operator. Trans. Amer. Math. Soc. 312
(1989), no. 1, 115--128. (Reviewer: Hitoshi Kitada) 35P15 (26D10 35J10
47F05)
- 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)
- 89g:46068 Schechter, Martin Potential estimates in Orlicz
spaces. Pacific J. Math. 133 (1988), no. 2,
381--399. (Reviewer: Bruno Franchi) 46E35 (26D15 35G30)
- 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)
- 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-New York, 1986.
xiv+310 pp. ISBN: 0-444-87822-X (Reviewer: A. Devinatz) 35Pxx (47F05)
- 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)
- 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)
- 87d:49030 Schechter, Martin Derivatives of mappings with
applications to nonlinear differential
equations. Trans. Amer. Math. Soc. 293 (1986), no. 1, 53--69. (Reviewer:
PZer TallŅs) 49A52 (46G05)
- 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-New
York, 1984. 47Bxx (35R20 47Axx 47Hxx 58G99)
- 86g:46062 Schechter, Martin Differentiation in abstract
spaces. J. Differential Equations 55 (1984),
no. 3, 330--345. (Reviewer: A. B. NZeth) 46G05 (58C20)
- 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)
- 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)
- 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)
- 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)
- 83a:47011 Schechter, Martin Wave operators for pairs of spaces
and the Klein\mhy Gordon equation.
Aequationes Math. 20 (1980), no. 1, 38--50. (Reviewer: H. BaumgStel)
47A40 (35P25 81F05)
- 82h:81095 Schechter, M.; Weder, R. A theorem on the existence
of dyon solutions. Ann. Physics 132
(1981), no. 2, 292--327. (Reviewer: JosZM. CerverŅ) 81E10 (58E30)
- 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
- 81k:47014 Schechter, Martin The continuous singular spectrum
of the Schrsinger operator. Math.
Proc. Cambridge Philos. Soc. 88 (1980), no. 1, 59--69. (Reviewer: W.
Allegretto) 47A40 (35P05 81C10)
- 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)
- 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)
- 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)
- 80i:47012 Schechter, Martin Completeness of wave operators in
two Hilbert spaces. Ann. Inst. H.
PoincarZSect. A (N.S.) 30 (1979), no. 2, 109--127. (Reviewer: P. A.
Mishnaevski\u \i) 47A40
- 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)
- 80c:47013 Schechter, Martin The invariance principle. Comment.
Math. Helv. 54 (1979), no. 1,
111--125. (Reviewer: M. M. Skriganov) 47A40 (35P25)
- 80c:47012 Schechter, Martin Another look at scattering theory.
Internat. J. Theoret. Phys. 17 (1978),
no. 1, 33--41. (Reviewer: M. M. Skriganov) 47A40
- 80c:35078 Schechter, Martin Scattering theory for the
Schrsinger 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)
- 58 #23156 Schechter, Martin Essential self-adjointness of the
Schrsinger operator with magnetic vector
potential. J. Functional Analysis 20 (1975), no. 2, 93--104. 35P05
- 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)
- 58 #17586 Koller, Herbert; Schechter, Martin; Weder, Ricardo
A. Schrsinger operators in the uniform
norm. Ann. Inst. H. PoincarZSect. A (N.S.) 26 (1977), no. 3, 303--311.
(Reviewer: Richard B. Lavine) 35P05
(35J10)
- 58 #17436 Schechter, Martin Modern methods in partial
differential equations. An introduction.
McGraw-Hill International Book Co., New York-Bogotā-Auckland, 1977.
xiv+245 pp. ISBN: 0-07-055193-6
(Reviewer: Ju. V. Kostarcuk) 35-01
- 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
- 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)
- 57 #17027 Schechter, Martin Discreteness of the singular
spectrum for Schrsinger operators. Math.
Proc. Cambridge Philos. Soc. 80 (1976), no. 1, 121--133. 35P25 (47A40)
- 57 #10275 Schechter, Martin Nonhomogeneous elliptic systems
and scattering. TĒhoku Math. J. (2) 27
(1975), no. 4, 601--616. 35P25 (35J45 47A40)
- 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
- 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)
- 57 #917 Schechter, Martin The Klein-Gordon equation and
scattering theory. Ann. Physics 101
(1976), no. 2, 601--609. (Reviewer: Teruo Ikebe) 35P25
- 57 #914 Schechter, Martin Scattering theory for elliptic
systems. J. Math. Soc. Japan 28 (1976), no. 1,
71--79. (Reviewer: J. Thomas Beale) 35P20
- 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
- 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
- 56 #3607 Schechter, Martin Principles of functional analysis.
Academic Press, New York-London,
1971. xix+383 pp. 46-01 (47-01)
- 55 #13097 Schechter, Martin Eigenfunction expansions for the
Schrsinger operator. Ark. Mat. 14
(1976), no. 2, 277--287. (Reviewer: M. M. Skriganov) 35P10 (35J10)
- 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)
- 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)
- 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
- 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)
- 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)
- 53 #13865 Schechter, Martin On the spectra of singular
elliptic operators. Mathematika 23 (1976), no.
1, 107--115. (Reviewer: J. R. Kuttler) 35P15
- 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)
- 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
- 51 #6450 Schechter, Martin Proper boundary points of the
spectrum. Osaka J. Math. 12 (1975),
41--44. (Reviewer: C. R. Putnam) 47A10
- 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
- 51 #3726 Schechter, Martin Scattering theory for elliptic
operators of arbitrary order. Comment.
Math. Helv. 49 (1974), 84--113. (Reviewer: C. Bardos) 35P25
- 51 #1436 Schechter, Martin A unified approach to scattering.
J. Math. Pures Appl. (9) 53 (1974),
373--396. (Reviewer: T. Kato) 47A40 (35P25)
- 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
- 48 #4773 Schechter, Martin Operators obeying Weyl's theorem.
Scripta Math. 29, 67--75. (1973).
(Reviewer: K. K. Oberai) 47A10
- 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)
- 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)
- 46 #4280 Schechter, Martin Hamiltonians for singular
potentials. Indiana Univ. Math. J. 22
(1972/73), 483--503. (Reviewer: B. Hellwig) 47F05 (35P99)
- 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)
- 45 #4171 Schechter, Martin Quantities related to strictly
singular operators. Indiana Univ. Math. J.
21 (1971/72), 1061--1071. (Reviewer: J. D. Gray) 47B99
- 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)
- 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)
- 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)
- 41 #5992 Dash, A. T.; Schechter, M. Tensor products and joint
spectra. Israel J. Math. 8 1970
191--193. (Reviewer: C. Pearcy) 47.30
- 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
- 41 #2431 Schechter, Martin On the spectra of operators on
tensor products. J. Functional Analysis 4
1969 95--99. (Reviewer: A. Brown) 47.30
- 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)
- 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)
- 40 #3348 Lebow, Arnold; Schechter, Martin Norms on quotient
spaces. Bull. Amer. Math. Soc. 75
1969 1322--1325. (Reviewer: S. Goldberg) 47.40
- 40 #1809 Schechter, Martin On perturbations of essential
spectra. J. London Math. Soc. (2) 1 1969
343--347. (Reviewer: K. Gustafson) 47.48
- 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)
- 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
- 37 #6777 Schechter, Martin Riesz operators and Fredholm
perturbations. Bull. Amer. Math. Soc. 74
1968 1139--1144. (Reviewer: S. R. Caradus) 47.10
- 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
- 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)
- 36 #6977 Schechter, Martin Basic theory of Fredholm
operators. Ann. Scuola Norm. Sup. Pisa (3) 21
1967 261--280. (Reviewer: S. Goldberg) 47.45
- 36 #6927 Schechter, Martin Complex interpolation. Compositio
Math. 18 1967 117--147 (1967).
(Reviewer: J. Peetre) 46.38
- 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)
- 35 #3486 Schechter, Martin Essential spectra of elliptic
partial differential equations. Bull. Amer.
Math. Soc. 73 1967 567--572. (Reviewer: C. Clark) 47.65
- 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
- 33 #6146 Schechter, Martin Nonlocal elliptic boundary value
problems. Ann. Scuola Norm. Sup. Pisa
(3) 20 1966 421--441. (Reviewer: Colin Clark) 35.45
- 33 #6094 Schechter, Martin On the theory of differential
boundary problems. Illinois J. Math. 7 1963
232--245. (Reviewer: R. S. Freeman) 35.31
- 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)
- 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
- 32 #6052 Schechter, Martin On $L\sp{p}$ estimates and
regularity. II. Math. Scand. 13 1963 47--69.
(Reviewer: R. Beals) 35.19
- 32 #6051 Schechter, Martin On $L\sp{p}$ estimates and
regularity. I. Amer. J. Math. 85 1963 1--13.
(Reviewer: R. Beals) 35.19
- 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
- 32 #6049 Schechter, Martin On the dominance of partial
differential operators. Trans. Amer. Math.
Soc. 107 1963 i37--260. (Reviewer: R. Carroll) 35.39
- 31 #3713 Schechter, Martin On $L\sp{p}$ estimates and
regularity. III. Ricerche Mat. 13 1964
192--206. (Reviewer: J. Peetre) 35.24
- 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)
- 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)
- 30 #5167 Schechter, Martin Invariance of the essential
spectrum. Bull. Amer. Math. Soc. 71 1965
365--367. (Reviewer: T. Kato) 47.10 (47.48)
- 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
- 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
- 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)
- 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
- 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)
- 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
- 28 #1381 Schechter, Martin A local regularity theorem. J.
Math. Mech. 10 1961 279--287.
(Reviewer: W. F. Donoghue, Jr.) 35.45
- 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
- 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
- 26 #4210 Schechter, Martin Coerciveness in $L\sp{p}$. Trans.
Amer. Math. Soc. 107 1963 10--29.
(Reviewer: J. Horvāth) 47.65 (35.99)
- 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
- 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
- 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
- 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
- 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)
- 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
- 23 #A2636 Schechter, Martin Negative norms and boundary
problems. Ann. of Math. (2) 72 1960
581--593. (Reviewer: E. Magenes) 35.45
- 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
- 23 #A2634 Schechter, Martin Mixed boundary problems for
general elliptic equations. Comm. Pure
Appl. Math. 13 1960 183--201. (Reviewer: E. Magenes) 35.45
- 23 #A2633 Schechter, Martin Remarks on elliptic boundary
value problems. Comm. Pure Appl.
Math. 12 1959 561--578. (Reviewer: E. Magenes) 35.45
- 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
- 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
- 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
- 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)
- 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
- 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
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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