Universal hierarchical structure of quasiperiodic eigenfunctions S Jitomirskaya, W Liu
Annals of Mathematics 187 (3), 721-776, 2018
77 2018 Arithmetic spectral transitions for the Maryland model S Jitomirskaya, W Liu
Communications on Pure and Applied Mathematics 70 (6), 1025-1051, 2017
47 2017 Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase S Jitomirskaya, W Liu
Journal of the European Mathematical Society, 2023
41 2023 Anderson localization for multi-frequency quasi-periodic operators on S Jitomirskaya, W Liu, Y Shi
Geometric and Functional Analysis 30 (2), 457-481, 2020
31 2020 Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues W Liu
Geometric and Functional Analysis 32 (1), 1-30, 2022
20 2022 Quantitative inductive estimates for Green’s functions of non-self-adjoint matrices W Liu
Analysis & PDE 15 (8), 2061-2108, 2023
18 2023 Irreducibility of the Bloch variety for finite-range Schrödinger operators J Fillman, W Liu, R Matos
Journal of Functional Analysis 283 (10), 109670, 2022
18 2022 Criteria for embedded eigenvalues for discrete Schrödinger operators W Liu
International Mathematics Research Notices 2021 (20), 15803-15832, 2021
17 2021 Spectral gaps of almost Mathieu operators in the exponential regime W Liu, X Yuan
Journal of Fractal Geometry 2 (1), 1-51, 2015
15 2015 Anderson localization for the almost Mathieu operator in the exponential regime W Liu, X Yuan
Journal of Spectral Theory 5 (1), 89-112, 2015
14 2015 Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators W Liu, DC Ong
Journal d'Analyse Mathématique 141 (2), 625-661, 2020
13 2020 Anderson localization for the completely resonant phases W Liu, X Yuan
Journal of Functional Analysis 268 (3), 732-747, 2015
13 2015 Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian S Jitomirskaya, W Liu
Geometric and Functional Analysis 29, 238-257, 2019
12 2019 Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies W Liu, Y Shi
Journal of Spectral Theory 9 (4), 1223-1248, 2019
11 2019 Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators W Liu
Journal of Functional Analysis 276 (9), 2936-2967, 2019
11 2019 Fermi isospectrality for discrete periodic Schrodinger operators W Liu
arXiv preprint arXiv:2106.03726, 2021
10 2021 Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime W Liu, X Yuan
Journal of Mathematical Physics 56 (1), 2015
10 2015 Topics on Fermi varieties of discrete periodic Schrödinger operators W Liu
Journal of Mathematical Physics 63 (2), 023503, 2022
9 2022 Absence of singular continuous spectrum for perturbed discrete Schrödinger operators W Liu
Journal of Mathematical Analysis and Applications 472 (2), 1420-1429, 2019
9 2019 Upper bounds on transport exponents for long range operators S Jitomirskaya, W Liu
J. Math. Phys. 62 (2021), no. 7, Paper No. 073506, 9 pp., 2021
8 2021