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Fixed point formula for holomorphic functions

Author: Nikolai Tarkhanov
Journal: Proc. Amer. Math. Soc. 132 (2004), 2411-2419
MSC (2000): Primary 32S50; Secondary 58J20
Published electronically: March 24, 2004
MathSciNet review: 2052419
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Abstract: We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain $\mathcal{D}$ with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of $\mathcal{D}$, we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in $\mathcal{D}$ and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.

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Additional Information

Nikolai Tarkhanov
Affiliation: Institute of Mathematics, University of Potsdam, P.O. Box 60 15 53, 14415 Potsdam, Germany

Keywords: Lefschetz number, Neumann problem, Bergman kernel
Received by editor(s): January 30, 2003
Received by editor(s) in revised form: May 15, 2003
Published electronically: March 24, 2004
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2004 American Mathematical Society

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