Szego Coordinates, Quadrature Domains, and Double Quadrature Domains

作者：Bell Steven R^*; Gustafsson Bjorn; Sylvan Zachary A

来源：Computational Methods and Function Theory, 2011, 11(1): 25-44.

DOI：10.1007/BF03321788

• Bergman kernel
• Poisson kernel
• conformal mapping

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 C-infinity-smooth finitely connected domains.

• 出版日期2011