Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator
type: Item
instance of: scholarly article
title: Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator
zbMATH Open document ID: 1016.47014
DOI: 10.4171/ZAA/1053
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2002-07-22T00:00:00Z
review text: Summary: A family of self-adjoint compact operators \(A_\varepsilon\) \((\varepsilon>0)\) acting in Hilbert spaces \({\mathcal H}_\varepsilon\) is considered. The asymptotic behaviour as \(\varepsilon\to 0\) of eigenvalues and eigenvectors of the operators \(A_\varepsilon\) is studied; the limiting operator \(A_0:{\mathcal H}_0 \mapsto{\mathcal H}_0\) is non-compact. Asymptotic estimates of the differences between eigenvalues of \(A_\varepsilon\) and points of the spectrum \(\sigma(A_0)\) (both of the discrete spectrum and the essential one) are obtained. Asymptotic estimates for eigenvectors of \(A_\varepsilon\) are also proved.
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 47A75
zbMATH DE Number: 1747398
zbMATH Keywords: families of operators
zbMATH Keywords: domain perturbation
zbMATH Keywords: low frequency convergence
zbMATH Keywords: Hausdorff convergence of the spectrum
zbMATH Keywords: asymptotic estimates
zbMATH Keywords: perturbed operators
zbMATH Keywords: eigenvalue perturbation theory
zbMATH Keywords: self-adjoint compact operators in Hilbert spaces
zbMATH Keywords: spectrum
author: T. A. Mel'nik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1747398