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Research interests

Publications

  1. S. Jitomirskaya, W. Liu, Inhomogeneous Diophantine approximation in the coprime setting. Adv. Math. to appear. arXiv version
  2. S. Jitomirskaya, H. Krüger and W. Liu, Exact dynamical decay rate for the almost Mathieu operator. Math. Res. Lett. to appear. arXiv version
  3. W. Liu, Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function. Int. Math. Res. Not. IMRN to appear. arXiv version
  4. W. Liu, D. Ong, Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators. J. Anal. Math. to appear. arXiv version
  5. W. Liu, The asymptotical behaviour of the embedded eigenvalue for perturbed periodic operators. Pure Appl. Funct. Anal. to appear. arXiv version
  6. W. Liu, Y. Shi, Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies. J. Spectr. Theory to appear. arXiv version
  7. W. Liu, Almost Mathieu operators with with completely resonant phases. Ergodic Theory Dynam. Systems to appear. arXiv version
  8. W. Liu, Some refined results on the mixed Littlewood conjecture for pseudo-absolute values. J. Aust. Math. Soc. 107 (2019), no. 01, 91--109. arXiv version
  9. W. Liu, Letter to the Editor: Proof of the HRT conjecture for almost every (1,3) configuration. J. Fourier Anal. Appl. 25 (2019), no. 4, 1350--1360. arXiv version
  10. W. Liu, Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators. J. Funct. Anal. 276 (2019), no. 9, 2936--2967. arXiv version
  11. S. Jitomirskaya, W. Liu, Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian. Geom. Funct. Anal. 29 (2019), no. 1, 238--257. arXiv version
  12. W. Liu, Absence of singular continuous spectrum for perturbed discrete Schrödinger operators. J. Math. Anal. Appl. 472 (2019), no. 2, 1420--1429. arXiv version
  13. S. Jitomirskaya, W. Liu, Universal hierarchical structure of quasiperiodic eigenfunctions. Ann. of Math. (2) 187 (2018), no. 3, 721--776. arXiv version
  14. W. Liu, Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of initial energy. Math. Phys. Anal. Geom. 21 (2018), no. 3, 21:18. arXiv version
  15. W. Liu, Continuous quasiperiodic Schrödinger operators with Gordon type potentials. J. Math. Phys. 59 (2018), no. 6, 063501, 6 pp. arXiv version
  16. S. Jitomirskaya, W. Liu, Arithmetic spectral transitions for the Maryland model. CPAM(2017), no.6, 1025--1051. arXiv version
  17. S. Jitomirskaya, W. Liu, A Lower Bound on the Lyapunov Exponent for the Generalized Harper's Model. J. Stat. Phys. 166 (2017), no. 3-4, 609–-617. arXiv version
  18. W. Liu, The spectra of the surface Maryland model for all phases. Proc. Amer. Math. Soc. 144 (2016), no.12, 5035--5047. arXiv version
  19. W. Liu, X. Yuan, Anderson localization for the completely resonant phases. J. Funct. Anal. 268 (2015), no. 3, 732--747. arXiv version
  20. W. Liu, X. Yuan, Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime. J. Math. Phys. 56 (2015), no. 1, 012701, 21 pp. arXiv version
  21. W. Liu, X. Yuan, Spectral gaps of almost Mathieu operators in the exponential regime. J. Fractal Geom. 2 (2015), no. 1, 1--51. arXiv version
  22. W. Liu, X. Yuan, Anderson localization for the almost Mathieu operator in the exponential regime. J. Spectr. Theory 5 (2015), no. 1, 89--112. arXiv version
  23. W. Liu, Z. Huang, On the relationship of the spectra of the self-adjoint operator and its Liouville operator. Internat. J. Theoret. Phys. 52 (2013), no. 8, 2578--2591. Pdf
  24. W. Liu, Z. Huang, The generalized eigenvector expansions of the Liouville operator. Internat. J. Theoret. Phys. 52 (2013), no. 12, 4323--4334. Pdf
  25. S. Jitomirskaya, W. Liu, and S. Zhang, Arithmetic spectral transitions. To appear to AMS/PCMI, Harmonic Analysis, 2018 .

    26. Preprints

  26. S. Jitomirskaya, W. Liu, Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transitions in phase. arXiv version
  27. W. Liu, Criteria for embedded eigenvalues for discrete Schrödinger operators. arXiv version
  28. W. Liu, Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators. arXiv version
  29. W. Liu, The Möbius transformation of continued fractions with bounded upper and lower partial quotients. arXiv version

    30. Preprints in the final stages of preparation. Available upon request

  30. W. Liu, WKB and absence of singular continuous spectrum for perturbed periodic Schrödinger operators. Preprint
  31. S. Jitomirskaya, W. Liu, Noncompact complete Riemannian manifolds with singular continuous spectrum embedded in the essential spectrum of the Laplacian. Preprint
  32. S. Jitomirskaya, W. Liu and S. Tcheremchantsev, Wavepacket spreading and fractal spectral dimension of quasiperiodic operators with singular continuous spectrum. Preprint
  33. S. Jitomirskaya, W. Liu and L. Mi, Density of eigenfunctions for quasiperiodic operators. Preprint
  34. S. Jitomirskaya, W. Liu and Y. Shi, Anderson localization for high dimensional quasi-periodic operators with long-range interactions.Preprint

Notes

  • S. Jitomirskaya, W. Liu, Sharp Diophantine approximation in the inhomogeneous setting. Preprint.
  • W. Liu, Sharp bound on the largest positive eigenvalue for one-dimensional Schrödinger operators. arXiv version
  • W. Liu, X. Yuan, Absolutely continuous spectra for quasiperiodic Schrödinger operators in the exponential regime. arXiv version

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