On the singular Weyl-Titchmarsh function of perturbed spherical Schrodinger operators

被引：37

作者：

Kostenko, Aleksey ^{[2
,3
]}

Teschl, Gerald ^{[1
,4
]}

机构：

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

[2] NAS Ukraine, Inst Appl Math & Mech, UA-83114 Donetsk, Ukraine

[3] Dublin Inst Technol, Sch Math Sci, Dublin 8, Ireland

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 250卷 / 09期

基金：

奥地利科学基金会;

关键词：

Schrodinger operators; Bessel operators; Weyl-Titchmarsh theory; SELF-ADJOINT OPERATORS; SPECTRAL THEORY; PERTURBATIONS; EXTENSIONS;

D O I：

10.1016/j.jde.2010.10.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schrodinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) is an element of L-1(0,1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3701 / 3739

页数：39

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