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Izv. Vyssh. Uchebn. Zaved. Mat., 2008, Number 11, Pages 12–26 (Mi ivm1773)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression

V. M. Bruk

Saratov State Technical University

Abstract: We study invertible extensions of the minimal relation generated by a nonnegative operator function and a differential elliptic-type expression. We prove that the operators inverse to such extensions are integral operators and describe such integral operators. We obtain a formula for generalized resolvents of the minimal relation.

Keywords: linear relation, symmetric relation, generalized resolvent, Green function, operator function.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:11, 10–22

Bibliographic databases:

UDC: 517.983
Received: 31.08.2006

Citation: V. M. Bruk, “Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 11, 12–26; Russian Math. (Iz. VUZ), 52:11 (2008), 10–22

Citation in format AMSBIB
\Bibitem{Bru08}
\by V.~M.~Bruk
\paper Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 11
\pages 12--26
\mathnet{http://mi.mathnet.ru/ivm1773}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2530581}
\zmath{https://zbmath.org/?q=an:05533485}
\elib{https://elibrary.ru/item.asp?id=11526445}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 11
\pages 10--22
\crossref{https://doi.org/10.3103/S1066369X08110029}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Bruk, “On linear relations generated by nonnegative operator function and degenerate elliptic differential-operator expression”, Zhurn. matem. fiz., anal., geom., 5:2 (2009), 123–144  mathnet  mathscinet  zmath  elib
    2. V. M. Bruk, “On linear relations generated by a differential expression and by a Nevanlinna operator function”, Zhurn. matem. fiz., anal., geom., 7:2 (2011), 115–140  mathnet  mathscinet  zmath  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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