Szego坐标、quadrature域和双quadrature域
Szego coordinates, quadrature domains, and double quadrature domains
摘要：
我们定义Szego坐标上的光滑连接有界的平面域的效果的全纯变化的域上的坐标，可以接近的身份，如所需的，并转换域的正交域的边界弧长。当这些Szego坐标与Bergman坐标重合时，结果是关于面积和弧长的双重求积域。我们列举了主机的有趣和有用的属性，这样的双正交域拥有，我们表明，这样的域实际上是密集的境界有界的光滑边界的连通域。
英文摘要：
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.
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