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Quadrature domains and kernel function zipping

Steven R. Bell Mathematics Department, Purdue University

TBD mathscidoc:1701.333057

Arkiv for Matematik, 43, (2), 271-287, 2003.8
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.
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@inproceedings{steven2003quadrature,
  title={Quadrature domains and kernel function zipping},
  author={Steven R. Bell},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203614344336866},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={2},
  pages={271-287},
  year={2003},
}
Steven R. Bell. Quadrature domains and kernel function zipping. 2003. Vol. 43. In Arkiv for Matematik. pp.271-287. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203614344336866.
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