ASYMPTOTIC EXPANSION OF THE SPECTRUM FOR PERIODIC SCHRODINGER OPERATORS

被引：0

作者：

Armstrong, Scott ^{[1
]}

Venkatraman, Raghavendra ^{[1
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 02期

基金：

美国国家科学基金会;

关键词：

homogenization; Schro"dinger; spectrum; HOMOGENIZED EIGENVALUES; 1ST-ORDER CORRECTIONS; BOUNDARY-LAYERS;

D O I：

10.1137/22M1526228

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrodinger-type operator with a confining potential and with the principle part of a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order.

引用

页码：1770 / 1808

页数：39

共 50 条

[1] COMPLETE ASYMPTOTIC EXPANSION OF THE SPECTRAL FUNCTION OF MULTIDIMENSIONAL ALMOST-PERIODIC SCHRODINGER OPERATORS
Parnovski, Leonid
Shterenberg, Roman
[J]. DUKE MATHEMATICAL JOURNAL, 2016, 165 (03) : 509 - 561
[2] Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrodinger operators
Parnovski, Leonid
Shterenberg, Roman
[J]. ANNALS OF MATHEMATICS, 2012, 176 (02) : 1039 - 1096
[3] On absolute continuity of the spectrum of periodic Schrodinger operators
Seo, Ihyeok
[J]. MONATSHEFTE FUR MATHEMATIK, 2016, 180 (04): : 893 - 912
[4] Essential Spectrum of Schrodinger Operators on Periodic Graphs
Rabinovich, V. S.
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2018, 52 (01) : 66 - 69
[5] Characterization of the spectrum of Schrodinger operators with periodic distributions
Korotyaev, E
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2003, 2003 (37) : 2019 - 2031
[6] ASYMPTOTIC PROPERTIES OF POINT SPECTRUM FOR SOME SCHRODINGER OPERATORS
GUILLEMOTTEISSIER, M
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (08): : 419 - 421
[7] The spectrum of magnetic Schrodinger operators on a graph with periodic structure
Higuchi, Y
Shirai, T
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 169 (02) : 456 - 480
[8] ON THE SPECTRUM OF PERIODIC SCHRODINGER-OPERATORS AND A TOWER OF COVERINGS
ADACHI, T
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1995, 27 : 173 - 176
[9] Spectrum of Schrodinger operators with potential waveguides on periodic graphs
Saburova, N.
Post, O.
[J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE DAYS ON DIFFRACTION (DD) 2019, 2019, : 175 - 180
[10] On the Spectrum and Lyapunov Exponent of Limit Periodic Schrodinger Operators
Avila, Artur
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 288 (03) : 907 - 918

← 1 2 3 4 5 →