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Sibirsk. Mat. Zh., 2015, Volume 56, Number 4, Pages 878–895 (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

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.

DOI: https://doi.org/10.17377/smzh.2015.56.412

Full text: PDF file (363 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:4, 699–713

Bibliographic databases:

UDC: 517.984
Received: 28.10.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. H. Rasulov, N. A. Tosheva, “Analytic description of the essential spectrum of a family of 3X3 operator matrices”, Nanosyst.-Phys. Chem. Math., 10:5 (2019), 511–519  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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