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On the trace of certain rational operator functions

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Abstract

In this paper operator functions of type

$$L(\lambda ): = I - \sum\limits_{k = 1}^n {\lambda ^k } A_k + \sum\limits_{k = 1}^m {\frac{{\lambda ^{\varepsilon _k } }}{{(\lambda - a_k )^{\mu _k } }}H_k } $$

are considered. In the first part of the paper a linearization ofL is constructed, and it is shown that the geometric multiplicities and the null multiplicities of the eigenvalues λ ∈ χ ofL and the linearization coincide. In the second part of the paper trace and determinant formulas forL are derived under certain conditions for the coefficients ofL.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Fernuniversität-Gesamthochschule, Lützowstr. 125, Postfach 940, D-5800, Hagen, West Germany

    Hansjörg Linden & Josef Menzel

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  1. Hansjörg Linden
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  2. Josef Menzel
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Linden, H., Menzel, J. On the trace of certain rational operator functions. Integr equ oper theory 15, 30–42 (1992). https://doi.org/10.1007/BF01193765

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  • DOI: https://doi.org/10.1007/BF01193765

MSC 1991

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