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Mat. Zametki, 2017, Volume 101, Issue 4, Pages 516–530 (Mi mz10494)  

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

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.


DOI: https://doi.org/10.4213/mzm10494

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English version:
Mathematical Notes, 2017, 101:4, 619–630

Bibliographic databases:

UDC: 517
Received: 20.05.2014

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

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