On the Perturbation Theory of Self-Adjoint Operators

On the Perturbation Theory of Self-Adjoint Operators

Sergio ALBEVERIO, Sergei KUZHEL, and Leonid P. NIZHNIK

Source: Tokyo J. of Math. Volume 31, Number 2 (2008), 273-292.

Abstract

We show that all types of self-adjoint perturbations of a semi-bounded operator $A$ (purely singular, mixed singular, and regular) can be described and studied from a unique point of view in the framework of the extension theory as well as in the framework of the additive perturbation theory. We also show that any singular finite rank perturbation $\widetilde{A}$ can be approximated in the norm resolvent sense by regular finite rank perturbations of $A$. An application is given to the study of Schr\"{o}dinger operators with point interactions.

Primary Subjects: 47A10

Secondary Subjects: 47A55, 81Q10

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Permanent link to this document: http://projecteuclid.org/euclid.tjm/1233844052
Digital Object Identifier: doi:10.3836/tjm/1233844052
Mathematical Reviews number (MathSciNet): MR2477872
Zentralblatt MATH identifier: 05545412

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