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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 4, Pages 878–895
DOI: https://doi.org/10.17377/smzh.2015.56.412 (Mi smj2684) 		 
This article is cited in 1 scientific paper (total in 1 paper)

An eigenvalue multiplicity formula for the Schur complement of a $3\times3$ block operator matrix

M. É. Muminova, T. Kh. Rasulovb

a University of Technology, Skudai, Malaysia
b Bukhara State University, Bukhara, Uzbekistan
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DOI: https://doi.org/10.17377/smzh.2015.56.412
Abstract: We consider the Schur complement $S(\lambda)$ with real spectral parameter $\lambda$ corresponding to a certain $3\times3$ block operator matrix. In our case the essential spectrum of $S(\lambda)$ can have gaps. We obtain formulas for the number and multiplicities of eigenvalues belonging to an arbitrary interval outside the essential spectrum of $S(\lambda)$.
Keywords: Schur complement, bosonic Fock space, block operator matrix, creation and annihilation operators, trace class operator, essential and discrete spectra, Weyl's inequality.
Received: 28.10.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 4, Pages 699–713
DOI: https://doi.org/10.1134/S0037446615040126
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: M. É. Muminov, T. Kh. Rasulov, “An eigenvalue multiplicity formula for the Schur complement of a $3\times3$ block operator matrix”, Sibirsk. Mat. Zh., 56:4 (2015), 878–895; Siberian Math. J., 56:4 (2015), 699–713
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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    		Сибирский математический журнал Siberian Mathematical Journal
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