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

Loading next page...
 
/lp/springer_journal/quadrature-domains-for-the-bergman-space-in-several-complex-variables-MQNbVprkKZ
Publisher
Springer Berlin Heidelberg
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
D.O.I.
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

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off