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An eigenvalue multiplicity formula for the Schur complement of a 3 × 3 block operator matrix

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Abstract

We consider the Schur complement S(λ) with real spectral parameter λ corresponding to a certain 3 × 3 block operator matrix. In our case the essential spectrum of S(λ) can have gaps. We obtain formulas for the number and multiplicities of eigenvalues belonging to an arbitrary interval outside the essential spectrum of S(λ).

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Correspondence to M. É. Muminov.

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Original Russian Text Copyright © 2015 Muminov M. É. and Rasulov T.Kh.

The authors were supported by the Program of the Einstein Fund of the International Mathematical Society. The second author is grateful to the Berlin Mathematical School and the Weierstrass Institute for Applied Analysis and Stochastics for invitation, support, and hospitality.

Skudai; Bukhara. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 878–895, July–August, 2015; DOI: 10.17377/smzh.2015.56.412.

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Muminov, M.É., Rasulov, T.K. An eigenvalue multiplicity formula for the Schur complement of a 3 × 3 block operator matrix. Sib Math J 56, 699–713 (2015). https://doi.org/10.1134/S0037446615040126

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  • DOI: https://doi.org/10.1134/S0037446615040126

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