Spectral theory for slowly oscillating potentials .2. Schrodinger operators

被引：20

作者：

Stolz, G

机构：

[1] Department of Mathematics, University Alabama at Birmingham, Birmingham

来源：

MATHEMATISCHE NACHRICHTEN | 1997年 / 183卷

关键词：

Schrodinger operators; spectral theory; oscillating potentials;

D O I：

10.1002/mana.19971830116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The absolutely continuous and singular spectrum of one-dimensional Schrodinger operators with slowly oscillating potentials and perturbed periodic potentials is studied, continuing similar investigations for Jacobi matrices from [14]. Trace class methods are used to locate the singular spectrum. The absolutely continuous spectrum is determined by iterated diagonalization of transfer matrices to prove boundedness of eigensolutions.

引用

页码：275 / 294

页数：20

共 50 条

[31] A LOCAL SPECTRAL THEORY FOR OPERATORS .2.
STAMPFLI, JG
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 75 (04) : 803 - &
[32] SPECTRAL THEORY OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS WITH STRONGLY FLUCTUATING POTENTIALS
GORDON, AY
MOLCHANOV, SA
TSAGANI, B
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1991, 25 (03) : 236 - 238
[33] SPECTRAL ASYMPTOTICS FOR THE SCHRODINGER OPERATOR ON THE LINE WITH SPREADING AND OSCILLATING POTENTIALS
Duchene, Vincent
Raymond, Nicolas
DOCUMENTA MATHEMATICA, 2018, 23 : 599 - 636
[34] Spectral stability of Schrodinger operators with subordinated complex potentials
Fanelli, Luca
Krejcirik, David
Vega, Luis
JOURNAL OF SPECTRAL THEORY, 2018, 8 (02) : 575 - 604
[35] Spectral gaps of Schrodinger operators with periodic singular potentials
Djakov, Plamen
Mityagin, Boris
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2009, 6 (02) : 95 - 165
[36] SPECTRAL PROPERTIES OF SCHRODINGER-OPERATORS WITH MATRIX POTENTIALS
SEBA, P
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1984, 17 (08): : 1625 - 1630
[37] Perturbation of Schrodinger Operators by Complex-Valued Rapidly Oscillating Potentials
Oshime, Yorimasa
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2016, 59 (02): : 289 - 301
[38] Scattering and wave operators for one-dimensional Schrodinger operators with slowly decaying nonsmooth potentials
Christ, M
Kiselev, A
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2002, 12 (06) : 1174 - 1234
[39] Sum rules and spectral measures of Schrodinger operators with L2 potentials
Killip, Rowan
Simon, Barry
ANNALS OF MATHEMATICS, 2009, 170 (02) : 739 - 782
[40] Spectral Theory of Semibounded Schrodinger Operators with δ'-Interactions
Kostenko, Aleksey
Malamud, Mark
ANNALES HENRI POINCARE, 2014, 15 (03): : 501 - 541

← 1 2 3 4 5 →