UNIQUENESS RESULTS FOR ONE-DIMENSIONAL SCHRODINGER OPERATORS WITH PURELY DISCRETE SPECTRA

被引：0

作者：

Eckhardt, Jonathan ^{[1
]}

Teschl, Gerald ^{[1
,2
]}

机构：

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[2] Int Erwin Schrodinger Inst Math Phys, A-1090 Vienna, Austria

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2013年 / 365卷 / 07期

基金：

奥地利科学基金会;

关键词：

Schrodinger operators; inverse spectral theory; discrete spectra; PARTIAL INFORMATION; INVERSE PROBLEM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide an abstract framework for singular one-dimensional Schrodinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operator completely. As an example we apply our findings to prove new uniqueness results for perturbed quantum mechanical harmonic oscillators. In addition, we also show how to establish a Hochstadt-Lieberman type result for these operators. Our approach is based on the singular Weyl-Titchmarsh-Kodaira theory which is extended to cover the present situation.

引用

页码：3923 / 3942

页数：20

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