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Mat. Zametki, 2007, Volume 82, Issue 5, Pages 652–664 (Mi mz4080)  

This article is cited in 4 scientific papers (total in 4 papers)

On Invertible Contractions of Quotients Generated by a Differential Expression and by a Nonnegative Operator Function

V. M. Bruk

Saratov State Technical University

Abstract: In the present paper, we describe invertible contractions of the maximal quotient generated by a differential expression with bounded operator coefficients and by a nonnegative operator function. We show that the operators inverse to such contractions are integral operators and prove a criterion for such operators to be holomorphic. Using the results obtained, we describe the generalized resolvents of symmetric quotients.

Keywords: invertible contraction, integral operator, holomorphic operator, operator function, Hilbert space, self-adjoint operator, Borel measurable function

DOI: https://doi.org/10.4213/mzm4080

Full text: PDF file (497 kB)
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English version:
Mathematical Notes, 2007, 82:5, 583–595

Bibliographic databases:

UDC: 517.983.53
Received: 15.04.2005
Revised: 17.03.2007

Citation: V. M. Bruk, “On Invertible Contractions of Quotients Generated by a Differential Expression and by a Nonnegative Operator Function”, Mat. Zametki, 82:5 (2007), 652–664; Math. Notes, 82:5 (2007), 583–595

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v82/i5/p652

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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. Bruk V.M., “Erratum: “On invertible contractions of quotients generated by a differential expression and by a nonnegative operator function” [Mathematical Notes 82 (5–6), 583–595 (2007)]”, Math. Notes, 84:3–4 (2008), 449–450  crossref  isi  elib  scopus
    2. 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
    3. 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
    4. V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufa Math. J., 6:4 (2014), 48–59  mathnet  crossref
  • Математические заметки Mathematical Notes
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