Pseudomodes for Schrodinger operators with complex potentials

被引：14

作者：

Krejcirik, David ^{[1
]}

Siegl, Petr ^{[2
]}

机构：

[1] Czech Tech Univ, Dept Math, Fac Nucl Sci & Phys Engn, Trojanova 13, Prague 12000 2, Czech Republic

[2] Queens Univ Belfast, Sch Math & Phys, Univ Rd, Belfast BT7 1NN, Antrim, North Ireland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 276卷 / 09期

基金：

瑞士国家科学基金会;

关键词：

Pseudospectrum; Schrodinger operators; Complex potential; WKB; PSEUDOSPECTRA; SPECTRUM;

D O I：

10.1016/j.jfa.2018.10.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For one-dimensional Schrodinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. We develop a first systematic non-semi-classical approach, which results in a substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones. Applications of the present results to higher-dimensional Schrodinger operators are also discussed. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：2856 / 2900

页数：45

共 50 条

[41] ON SCHRODINGER OPERATORS WITH DYNAMICALLY DEFINED POTENTIALS
Goldstein, Michael
Schlag, Wilhelm
MOSCOW MATHEMATICAL JOURNAL, 2005, 5 (03) : 577 - 612
[42] SPECTRAL THEORY OF SCHRODINGER-OPERATORS WITH PERIODIC COMPLEX-VALUED POTENTIALS
PASTUR, LA
TKACHENKO, VA
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1988, 22 (02) : 156 - 158
[43] Lieb-Thirring inequalities for Schrodinger operators with complex-valued potentials
Frank, Rupert L.
Laptev, Ari
Lieb, Elliott H.
Seiringer, Robert
LETTERS IN MATHEMATICAL PHYSICS, 2006, 77 (03) : 309 - 316
[44] Trace formulae for Schrodinger operators with complex-valued potentials on cubic lattices
Korotyaev, Evgeny
Laptev, Ari
BULLETIN OF MATHEMATICAL SCIENCES, 2018, 8 (03) : 453 - 475
[45] Pseudomodes of Schrödinger operators
Krejcirik, David
Siegl, Petr
FRONTIERS IN PHYSICS, 2024, 12
[46] ESTIMATES OF EIGENVALUES OF SCHRODINGER OPERATORS ON THE HALF-LINE WITH COMPLEX-VALUED POTENTIALS
Enblom, Alexandra
OPERATORS AND MATRICES, 2017, 11 (02): : 369 - 380
[47] THE SOBOLEV INEQUALITIES ON REAL HYPERBOLIC SPACES AND EIGENVALUE BOUNDS FOR SCHRODINGER OPERATORS WITH COMPLEX POTENTIALS
Chen, Xi
ANALYSIS & PDE, 2022, 15 (08): : 1861 - 1878
[48] On Dirichlet-Schrodinger operators with strong potentials
Grillo, G
STUDIA MATHEMATICA, 1995, 116 (03) : 239 - 254
[49] Spectral properties of schrodinger operators with decaying potentials
Denisov, Sergey A.
Kiselev, Alexander
SPECTRAL THEORY AND MATHEMATICAL PHYSICS: A FESTSCHRIFT IN HONOR OF BARRY SIMON'S 60TH BIRTHDAY: ERGODIC SCHRODINGER OPERATORS, SINGULAR SPECTRUM, ORTHOGONAL POLYNOMIALS, AND INVERSE SPECTRAL THEORY, 2007, 76 : 565 - 589
[50] A Class of Schrodinger Operators with Decaying Oscillatory Potentials
Lukic, Milivoje
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 326 (02) : 441 - 458

← 1 2 3 4 5 →