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A generalization of the method of Hermitian forms and an application of it in the theory of separation of spectra of operator bundles

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Abstract

We establish a connection between the methods of Hermite, Schur, and Lyapunov in the theory of stability of polynomials. We state generalizations of the criterion for stability and the concept of the resultant and the Bezoutiant to polynomial operator bundles. We consider some questions in the factorization of operator bundles. We study certain classes of generalized spectral problems (linear with respect to the spectral parameter and multiparameter problems).

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Authors
  1. A. I. Balinskii
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 185–189.

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Balinskii, A.I. A generalization of the method of Hermitian forms and an application of it in the theory of separation of spectra of operator bundles. J Math Sci 67, 2999–3002 (1993). https://doi.org/10.1007/BF01095885

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  • DOI: https://doi.org/10.1007/BF01095885

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