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Matematicheskie Zametki, 2017, Volume 101, Issue 4, Pages 516–530
DOI: https://doi.org/10.4213/mzm10494 (Mi mzm10494) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Representation Theorems and Variational Principles for Self-Adjoint Operator Matrices

A. A. Vladimirov

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
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DOI: https://doi.org/10.4213/mzm10494
Abstract: We use the notion of triples $\mathfrak{D}^+\hookrightarrow \mathfrak{H}\hookrightarrow\mathfrak{D}^-$ of Hilbert spaces to develop an analog of the Friedrichs extension procedure for a class of nonsemibounded operator matrices. In addition, we suggest a general approach (stated in the same terms) to the construction of variational principles for the eigenvalues of such matrices.
Keywords: rigged space, operator matrix, self-adjoint extension, variational principle.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00706
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00706.
Received: 20.05.2014
English version:
Mathematical Notes, 2017, Volume 101, Issue 4, Pages 619–630
DOI: https://doi.org/10.1134/S0001434617030208
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. A. Vladimirov, “Representation Theorems and Variational Principles for Self-Adjoint Operator Matrices”, Mat. Zametki, 101:4 (2017), 516–530; Math. Notes, 101:4 (2017), 619–630
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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