Invertible linear relations generated by an integral equation with Nevanlinna measure
type: Item
instance of: scholarly article
title: Invertible linear relations generated by an integral equation with Nevanlinna measure
zbMATH Open document ID: 1266.45013
DOI: 10.3103/S1066369X13020023
author: V. M. Bruk
published in: Russian Mathematics
publication date: 2013-04-10T00:00:00Z
review text: The families of maximal and minimal relations generated by integral equations with Nevanlinna operator measure and non-selfadjoint operator measure are defined. The author proves that if a restriction of a maximal relation is continuously invertible, then the inverse operator is integral. The special case is considered when the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations. A theorem which establishes a sufficient condition for the validity of such implication is proved. As an application, the author considers the differential equations with singular potentials described by \textit{A. M. Savchuk} and \textit{A. A. Shkalikov} [Math. Notes 66, No. 6, 741--753 (1999); translation from Mat. Zametki 66, No. 6, 897--912 (1999; Zbl 0968.34072)].
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 32A10
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 32A22
Mathematics Subject Classification ID: 32A35
zbMATH DE Number: 6152675
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear relation
zbMATH Keywords: integral equation
zbMATH Keywords: holomorphic family of relations
zbMATH Keywords: resolvent convergence
zbMATH Keywords: Sturm-Liouville Operator
zbMATH Keywords: maximal and minimal relations
zbMATH Keywords: Nevanlinna operator measure
zbMATH Keywords: non-selfadjoint operator measure
zbMATH Keywords: integral operators
reviewed by: Denis Sidorov
MaRDI profile type: Publication
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full work available at URL: s1066369x13020023
OpenAlex ID: W2052755998
description: scientific article; zbMATH DE number 6152675