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 Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 2, Pages 16–29 (Mi ivm8771)

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

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.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 13–24

UDC: 517.983

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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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. V. Khrabustovskyi, “Analogs of Generalized Resolvents for Relations Generated by a Pair of Differential Operator Expressions One of which Depends on Spectral Parameter in Nonlinear Manner”, Zhurn. matem. fiz., anal., geom., 9:4 (2013), 496–535
2. V. M. Bruk, “On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case”, Zhurn. matem. fiz., anal., geom., 10:2 (2014), 163–188
3. V. M. Bruk, “On Linear Relations Generated by an Integro-Differential Equation with Nevanlinna Measure in the Infinite-Dimensional Case”, Math. Notes, 96:1 (2014), 10–25
4. V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufa Math. J., 6:4 (2014), 48–59
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