Linear relations generated by an integral equation with Nevanlinna operator measure
type: Item
instance of: scholarly article
title: Linear relations generated by an integral equation with Nevanlinna operator measure
zbMATH Open document ID: 1266.45014
DOI: 10.3103/S1066369X12100015
author: V. M. Bruk
published in: Russian Mathematics
publication date: 2013-04-19T00:00:00Z
review text: The families of maximal and minimal linear relations generated by an integral equation with Nevanlinna operator measure aredefined and their holomorphic property is proved. If a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. The constancy of deficiency indices of some integral and differential equations discussed by \textit{S. A. Orlov} [Izv. Akad. Nauk SSSR, Ser. Mat. 40, 593--644 (1976; Zbl 0337.34020)] are proved using the proposed theory.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 32A22
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6155569
zbMATH Keywords: integral equation
zbMATH Keywords: holomorphic family of relations
zbMATH Keywords: deficiency index
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear relation
zbMATH Keywords: Nevanlinna operator measure
reviewed by: Denis Sidorov
MaRDI profile type: Publication
cites work: Q3512357
cites work: Q5441100
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full work available at URL: s1066369x12100015
OpenAlex ID: W2164930229
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description: scientific article; zbMATH DE number 6155569