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 Zh. Mat. Fiz. Anal. Geom., 2014, Volume 10, Number 2, Pages 163–188 (Mi jmag587)

On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case

V. M. Bruk

Saratov State Technical University, 77 Politekhnicheskaya Str., Saratov 410054, Russia

Abstract: We define the families of maximal and minimal relations generated by an integral equation with a Nevanlinna operator measure in the infinite-dimensional case and prove their holomorphic property. We show that if the restrictions of maximal relations are continuously invertible, then the operators inverse to these restrictions are integral. By using these results, we prove the existence of the characteristic operator and describe the families of linear relations generating the characteristic operator.

Key words and phrases: Hilbert space, linear relation, integral equation, characteristic operator, Nevanlinna measure.

DOI: https://doi.org/10.15407/mag10.02.163

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MSC: 47A06, 47A10, 34B27
Revised: 20.08.2013
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Citation: V. M. Bruk, “On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case”, Zh. Mat. Fiz. Anal. Geom., 10:2 (2014), 163–188

Citation in format AMSBIB
\Bibitem{Bru14} \by V.~M.~Bruk \paper On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case \jour Zh. Mat. Fiz. Anal. Geom. \yr 2014 \vol 10 \issue 2 \pages 163--188 \mathnet{http://mi.mathnet.ru/jmag587} \crossref{https://doi.org/10.15407/mag10.02.163} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236966} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334662300001} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Ufa Math. J., 7:2 (2015), 115–136
2. V. M. Bruk, “Boundary value problems for integral equations with operator measures”, Probl. anal. Issues Anal., 6(24):1 (2017), 19–40
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