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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 2, Pages 16–29 (Mi ivm8771)  

This article is cited in 5 scientific papers (total in 5 papers)

Invertible linear relations generated by an integral equation with a Nevanlinna measure

V. M. Bruk

Chair of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia
Full-text PDF (262 kB) Citations (5)
References:
Abstract: We define families of maximal and minimal relations generated by integral equations with a Nevanlinna operator measure and a non-selfadjoint operator measure. We prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We establish a sufficient condition ensuring that the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations. The obtained results are applicable to differential equations with singular coefficients.
Keywords: Hilbert space, linear relation, integral equation, holomorphic family of relations, resolvent convergence.
Received: 22.01.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 2, Pages 13–24
DOI: https://doi.org/10.3103/S1066369X13020023
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
Citation: V. M. Bruk, “Invertible linear relations generated by an integral equation with a Nevanlinna measure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 2, 16–29; Russian Math. (Iz. VUZ), 57:2 (2013), 13–24
Citation in format AMSBIB
\Bibitem{Bru13}
\by V.~M.~Bruk
\paper Invertible linear relations generated by an integral equation with a~Nevanlinna measure
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 2
\pages 16--29
\mathnet{http://mi.mathnet.ru/ivm8771}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 2
\pages 13--24
\crossref{https://doi.org/10.3103/S1066369X13020023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878389574}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Full-text PDF :79
    References:60
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