# Journal of Operator Theory

Volume 39, Issue 2, Spring 1998 pp. 219-247.

Linearization, completeness, and spectral asymptotics for certain rational and meromorphic operator functions**Authors**: Hansjorg Linden

**Author institution:**Fachbereich Mathematik, Fernuniversitaet-Gesamthochschule, Postfach 940, Lutzowstr. 125, D-58048 Hagen, Germany

**Summary:**In this paper rational operator functions of type $$ L(\lambda) := I - \sum_{k=0}^n\lambda^k A_k + \sum_{k=1}^m{1\over\lambda - a_k}H_k $$ are considered. With the aid of a linearization of $L$ results on the completeness of the eigenvectors and associated vectors, and spectral asymptotics are given. The results are extended to certain meromorphic operator functions.

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