Szegö coordinates, quadrature domains, and double quadrature domains
2011 (English)In: Computational methods in Function Theory, ISSN 1617-9447, Vol. 11, no 1, 25-44 p.Article in journal (Refereed) Published
We define Szegö coordinates on a finitely connected smoothly bounded planar domain which effect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When these Szegö coordinates coincide with Bergman coordinates, the result is a double quadrature domain with respect to both area and arc length. We enumerate a host of interesting and useful properties that such double quadrature domains possess, and we show that such domains are in fact dense in the realm of bounded C∞-smooth finitely connected domains.
Place, publisher, year, edition, pages
Heldermann Verlag , 2011. Vol. 11, no 1, 25-44 p.
Bergman kernel, Poisson kernel, conformal mapping
IdentifiersURN: urn:nbn:se:kth:diva-78758DOI: 10.1007/BF03321788ISI: 000311138000003ScopusID: 2-s2.0-84863203792OAI: oai:DiVA.org:kth-78758DiVA: diva2:492880
QC 201202162012-02-082012-02-082014-01-14Bibliographically approved