Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces

被引：6

作者：

Behrndt, Jussi ^{[1
]}

Leben, Leslie ^{[2
]}

Martinez Peria, Francisco ^{[3
,4
]}

Moews, Roland ^{[2
]}

Trunk, Carsten ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Numer Math, Steyrergasse 30, A-8010 Graz, Austria

[2] Tech Univ Ilmenau, Inst Math, Postfach 100565, D-98684 Ilmenau, Germany

[3] Univ Nacl La Plata, Dept Matemat, Fac Ciencias Exactas, CC 172, RA-1900 La Plata, Buenos Aires, Argentina

[4] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat Alberto P Calderon, Saavedra 15, RA-1083 Buenos Aires, DF, Argentina

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 439卷 / 02期

基金：

奥地利科学基金会;

关键词：

Selfadjoint operator; Krein space; Rank one perturbation; Eigenvalue estimates; Indefinite Sturm-Liouville operator; GENERALIZED NEVANLINNA FUNCTIONS; SELF-ADJOINT EXTENSIONS; LINEAR RELATION; DEFECT ONE; FACTORIZATION; SPECTRUM;

D O I：

10.1016/j.jmaa.2016.03.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A and B be selfadjoint operators in a Krein space and assume that the resolvent difference of A and B is of rank one. In the case that A is nonnegative and I is an open interval such that sigma(A) boolean AND I consists of isolated eigenvalues we prove sharp estimates on the number and multiplicities of eigenvalues of B in I. The general result is illustrated with eigenvalue estimates for singular indefinite Sturm-Liouville problems. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：864 / 895

页数：32

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