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On spectral properties of multiparameter polynomial matrices

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Abstract

Spectral problems for multiparameter polynomial matrices are considered. The notions of the spectrum (including those of its finite, infinite, regular, and singular parts), of the analytic multiplicity of a point of the spectrum, of bases of null-spaces, of Jordan s-semilattices of vectors and of generating vectors, and of the geometric and complete geometric multiplicities of a point of the spectrum are introduced. The properties of the above characteristics are described. A method for linearizing a polynomial matrix (with respect to one or several parameters) by passing to the accompanying pencils is suggested. The interrelations between spectral characteristics of a polynomial matrix and those of the accompanying pencils are established. Bibliography: 12 titles.

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Authors
  1. V. B. Khazanov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 284–321.

Translated by V. B. Khazanov.

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Khazanov, V.B. On spectral properties of multiparameter polynomial matrices. J Math Sci 89, 1775–1800 (1998). https://doi.org/10.1007/BF02355378

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  • DOI: https://doi.org/10.1007/BF02355378

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