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Zh. Mat. Fiz. Anal. Geom., 2011, Volume 7, Number 2, Pages 115–140 (Mi jmag508)  

This article is cited in 3 scientific papers (total in 3 papers)

On linear relations generated by a differential expression and by a Nevanlinna operator function

V. M. Bruk

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

Abstract: The families of maximal and minimal relations generated by a differential expression with bounded operator coefficients and by a Nevanlinna operator function are defined. These families are proved to be holomorphic. In the case of finite interval, the space of boundary values is constructed. In terms of boundary conditions, a criterion for the restrictions of maximal relations to be continuously invertible and a criterion for the families of these restrictions to be holomorphic are given. The operators inverse to these restrictions are stated to be integral operators. By using the results obtained, the existence of the characteristic operator on the finite interval and the axis is proved.

Key words and phrases: Hilbert space, linear relation, differential expression, holomorphic family of relations, resolvent, characteristic operator, Nevanlinna function.

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Bibliographic databases:
MSC: 47A06, 47A10, 34B27
Received: 22.04.2010
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Citation: V. M. Bruk, “On linear relations generated by a differential expression and by a Nevanlinna operator function”, Zh. Mat. Fiz. Anal. Geom., 7:2 (2011), 115–140

Citation in format AMSBIB
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\by V.~M.~Bruk
\paper On linear relations generated by a differential expression and by a~Nevanlinna operator function
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2011
\vol 7
\issue 2
\pages 115--140
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2829612}
\zmath{https://zbmath.org/?q=an:05955680}
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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. M. Bruk, “Invertible linear relations generated by an integral equation with a Nevanlinna measure”, Russian Math. (Iz. VUZ), 57:2 (2013), 13–24  mathnet  crossref
    2. 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  mathnet  mathscinet
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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