caa a22 4500 469043547 CHVBK 20180323132817.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF01195780 doi (NATIONALLICENCE)springer-10.1007/BF01195780 Linden Hansjörg Fachbereich Mathematik und Informatik, Fernuniversität-Gesamthochschule, Lützowstr. 125, Postfach 940, D-5800, Hagen, Germany aut Linearization, trace, and determinant of certain meromorphic operator functions [Elektronische Daten] [Hansjörg Linden] In this paper operator functions of type $$L(\lambda ): = I - \sum\limits_{k = 0}^\infty {\lambda ^{k + 1} A_k } + \sum\limits_{k = 0}^\infty {\tfrac{{\lambda ^{ \in _k } }}{{(\lambda - a_k )^{\mu _k } }}H_k } $$ are considered. In the first part of the paper a linearization ofL is constructed under certain convergence conditions, and it is shown that the geometric multiplicities and the null multiplicities of the eigenvalues λ ∈ ℂ ofL and the linearization coincide. In the second part of the paper trace and determinant formulas forL are derived under some further conditions for the coefficients ofL. Birkhäuser Verlag, 1992 Primary, 47 A 56 nationallicence Secondary, 47 B 10 nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag 15/4(1992-07-01), 568-588 0378-620X 15:4<568 1992 15 20 https://doi.org/10.1007/BF01195780 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01195780 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Linden Hansjörg Fachbereich Mathematik und Informatik, Fernuniversität-Gesamthochschule, Lützowstr. 125, Postfach 940, D-5800, Hagen, Germany aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/4(1992-07-01), 568-588 0378-620X 15:4<568 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer