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The Szegö Kernel and Proper Holomorphic Mappings to a Half Plane

The Szegö Kernel and Proper Holomorphic Mappings to a Half Plane We prove that all proper holomorphic mappings from a finitely connected domain in the plane to the right half plane can be expressed simply in terms of the Szegö kernel associated to the domain. Our decomposition also reveals the linear structure of the semi-group of all such maps and it offers a method to construct proper holomorphic maps of arbitrary mapping degree. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

The Szegö Kernel and Proper Holomorphic Mappings to a Half Plane

Computational Methods and Function Theory , Volume 11 (1) – Nov 17, 2010

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References (33)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321796
Publisher site
See Article on Publisher Site

Abstract

We prove that all proper holomorphic mappings from a finitely connected domain in the plane to the right half plane can be expressed simply in terms of the Szegö kernel associated to the domain. Our decomposition also reveals the linear structure of the semi-group of all such maps and it offers a method to construct proper holomorphic maps of arbitrary mapping degree.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Nov 17, 2010

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