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Mat. Zametki, 1977, Volume 22, Issue 6, Pages 825–834 (Mi mz8104)  

This article is cited in 6 scientific papers (total in 6 papers)

Extensions of symmetric relations

V. M. Bruk

Information and Computation Center of the Transportation of the Volga Region

Abstract: Maximal accretive and dissipative extensions of symmetric relations defined by abstract boundary conditions are considered in Hilbert space. Under the assumption that the resolvent of some extension has properties such as belonging to the Neumann–Shatten ideal or having given asymptotics of the $s$-numbers, either sufficient or necessary and sufficient conditions are found for a perturbation of the boundary conditions guaranteeing that the above properties are preserved for the resolvent of the perturbed extension.

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English version:
Mathematical Notes, 1977, 22:6, 953–958

Bibliographic databases:

UDC: 517.4
Received: 17.06.1976

Citation: V. M. Bruk, “Extensions of symmetric relations”, Mat. Zametki, 22:6 (1977), 825–834; Math. Notes, 22:6 (1977), 953–958

Citation in format AMSBIB
\Bibitem{Bru77}
\by V.~M.~Bruk
\paper Extensions of symmetric relations
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 6
\pages 825--834
\mathnet{http://mi.mathnet.ru/mz8104}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487580}
\zmath{https://zbmath.org/?q=an:0379.47010}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 6
\pages 953--958
\crossref{https://doi.org/10.1007/BF01099564}


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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. A. N. Kochubei, “Elliptic operators with boundary conditions on a subset of measure zero”, Funct. Anal. Appl., 16:2 (1982), 137–139  mathnet  crossref  mathscinet  zmath  isi
    2. Ufa Math. J., 7:2 (2015), 115–136  mathnet  crossref  isi  elib
    3. Koshmanenko V., Dudkin M., “Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators”, Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, Operator Theory Advances and Applications, 253, Springer Int Publishing Ag, 2016, 1–237  crossref  isi
    4. V. M. Bruk, “On self-adjoint and invertible linear relations generated by integral equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 1, 106–121  mathnet
    5. Mogilevskii I V., “On Couplings of Symmetric Operators With Possibly Unequal and Infinite Deficiency Indices”, Oper. Matrices, 14:1 (2020), 33–69  crossref  isi
    6. Vladislav M. Bruk, “Dissipative extensions of linear relations generated by integral equations with operator measures”, Zhurn. matem. fiz., anal., geom., 16:4 (2020), 381–401  mathnet  crossref
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