2010/03/10 by Steven R. Bell, Björn Gustafsson, Gustafsson, Steven R. Bell. Bjorn +3
Mathematics · #30C35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1003.2195
openalex publication_date 2010/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define Szego 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 Szego 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 finitely connected domains with smooth boundaries.