Spectral approximations of unbounded nonselfadjoint operators

Michael Gil’

doi:10.1007/s13324-012-0037-2

Spectral approximations of unbounded nonselfadjoint operators

Michael Gil’

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider the operator A=S+B, where S is an unbounded normal operator in a separable Hilbert space H, having a compact inverse one and B is a linear operator in H, such that BS^-1 is compact. Let (Formula presented.) be the normalized eigenvectors of S and B be represented in (Formula presented.) by a matrix (Formula presented.) We approximate the eigenvalues of A by a combination of the eigenvalues of S and the eigenvalues of the finite matrix (Formula presented.) Applications of to differential operators are also discussed.

Original language	English
Pages (from-to)	37-44
Number of pages	8
Journal	Analysis and Mathematical Physics
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s13324-012-0037-2
State	Published - 25 Mar 2013

Keywords

Approximation
Differential operators
Eigenvalues
Hilbert space
Linear operators

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-012-0037-2

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AB - We consider the operator A=S+B, where S is an unbounded normal operator in a separable Hilbert space H, having a compact inverse one and B is a linear operator in H, such that BS-1 is compact. Let (Formula presented.) be the normalized eigenvectors of S and B be represented in (Formula presented.) by a matrix (Formula presented.) We approximate the eigenvalues of A by a combination of the eigenvalues of S and the eigenvalues of the finite matrix (Formula presented.) Applications of to differential operators are also discussed.

KW - Approximation

KW - Differential operators

KW - Eigenvalues

KW - Hilbert space

KW - Linear operators

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JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 1

ER -

Spectral approximations of unbounded nonselfadjoint operators

Abstract

Keywords

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