A domain integral equation for the Bergman kernel
type: Item
instance of: scholarly article
title: A domain integral equation for the Bergman kernel
zbMATH Open document ID: 0921.30006
DOI: 10.1007/BF03322030
author: K. Appert
published in: Results in Mathematics
publication date: 1999-10-03T00:00:00Z
review text: This paper is devoted to these integral operators which have a reproducing property. The authors consider special representations of the Szegő, the Bergman and the Cauchy kernels. In generalization of Henrici's function-theoretic approach they obtained a boundary integral equation of the second-order for the Bergman kernel. For this reason it is necessary to construct an analogue to the Cauchy transform with a non-hermitean kernel. This transform is called \(\widehat{B}\)-transform. The construction is lined out for some important example: circle, oval of Cassini and ellipse. In some sense there now exists a similar result for the Bergman kernel to earlier statements for the Szegő kernel by E. Stein, N. Kerzman. The reader can find in this interesting paper a lot of further details on kernel functions of this type.
Mathematics Subject Classification ID: 30C40
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 46E22
zbMATH DE Number: 1294490
zbMATH Keywords: Szegő kernel
zbMATH Keywords: Cauchy kernels
zbMATH Keywords: Bergman kernel
zbMATH Keywords: kernel functions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322030
OpenAlex ID: W1975282425
description: scientific article; zbMATH DE number 1294490