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Quadrature Domains for the Bergman Space in Several Complex Variables

Quadrature Domains for the Bergman Space in Several Complex Variables We make use of the Bergman kernel function to study quadrature domains whose quadrature identities hold for $$L^2$$ L 2 holomorphic functions of several complex variables. We generalize some mapping properties of planar quadrature domains and point out some differences from the planar case. We then show that every smooth bounded convex domain in $${\mathbb {C}}^n$$ C n is biholomorphic to a quadrature domain. Finally, the possibility of continuous deformations within the class of planar quadrature domains is examined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Quadrature Domains for the Bergman Space in Several Complex Variables

Computational Methods and Function Theory , Volume 18 (2) – Nov 22, 2017

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0224-0
Publisher site
See Article on Publisher Site

Abstract

We make use of the Bergman kernel function to study quadrature domains whose quadrature identities hold for $$L^2$$ L 2 holomorphic functions of several complex variables. We generalize some mapping properties of planar quadrature domains and point out some differences from the planar case. We then show that every smooth bounded convex domain in $${\mathbb {C}}^n$$ C n is biholomorphic to a quadrature domain. Finally, the possibility of continuous deformations within the class of planar quadrature domains is examined.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Nov 22, 2017

References