Eigenvalue asymptotics of perturbed selfadjoint operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 1243.47032
author: A. A. Shkalikov
publication date: 2012-07-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.5204
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 6056410
zbMATH Keywords: perturbations of selfadjoint operators
zbMATH Keywords: eigenvalue asymptotics
MaRDI profile type: Publication
arXiv ID: 1202.5204
arXiv classification: math.SP
title: Eigenvalue asymptotics of perturbed selfadjoint operators
published in: Methods of Functional Analysis and Topology
review text: The author studies perturbations of a selfadjoint positive operator \(T\) satisfying the \(\alpha\)-non-condenseness condition (\(\alpha >0\)): NEWLINE\[NEWLINE n(t^{1/\alpha}+0,T)-n((t-1)^{1/\alpha},T)\leq l\quad \text{for some } l\in \mathbb N, NEWLINE\]NEWLINE where \(n(r,T)\) is the number of eigenvalues of \(T\) on \((0,r)\) including their multiplicity.NEWLINENEWLINEConditions on a perturbation \(B\) are found under which NEWLINE\[NEWLINE | n(r,T)-n(r,T+B)| \leq C[n(r+ar^\gamma ,T)-n(r-ar^\gamma ,T)]+C_1 NEWLINE\]NEWLINE for some positive constants \(C,C_1,a\), and \(\gamma \in [0,1)\).
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6056410