Quadrature域和核函数压缩
Quadrature domains and kernel function zipping
摘要：
证明了在平面上光滑有界多连通域中，求积域在很强的意义上是普遍存在的。事实上，它们是如此稠密，以至于人们不妨假设任何给定的光滑域都是一个正交域，这允许访问与该域相关的经典核函数上的大量强条件。遵循这一系列的想法，我们发现伯格曼内核可以压缩到一个惊人的小数据集。证明了与求积区域相关的核函数必须是代数的。
英文摘要：
It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
