ON THE DISTRIBUTION OF THE DISCRETE SPECTRUM OF NUCLEARLY PERTURBED OPERATORS IN BANACH SPACES

被引：2

作者：

Demuth, Michael ^{[1
]}

Hanauska, Franz ^{[1
]}

机构：

[1] Tech Univ Clausthal, Inst Math, D-38678 Clausthal Zellerfeld, Germany

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2015年 / 46卷 / 04期

关键词：

Eigenvalues; discrete spectrum; nuclear perturbations; COMPLEX JACOBI MATRICES; SCHRODINGER-OPERATORS; POTENTIALS; EIGENVALUES; BOUNDS; INEQUALITIES;

D O I：

10.1007/s13226-015-0145-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Z(0) be a bounded operator in a Banach space X with purely essential spectrum and K a nuclear operator in X. We construct a holomorphic function the zeros of which coincide with the discrete spectrum of Z(0)+K and derive a Lieb-Thirring type inequality. We obtain estimates for the number of eigenvalues in certain regions of the complex plane and an estimate for the asymptotics of the eigenvalues approaching to the essential spectrum of Z(0).

引用

页码：441 / 462

页数：22

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