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Martin boundaries of sectorial domains

Michael C. Cranston Department of Mathematics, University of Rochester Thomas S. Salisbury Department of Mathematics and Statistics, York University

TBD mathscidoc:1701.332782

Arkiv for Matematik, 31, (1), 27-49, 1991.8
Let$D$be a domain in$R$^{2}whose complement is contained in a pair of rays leaving the origin. That is,$D$contains two sectors whose base angles sum to 2π. We use balayage to give an integral test that determines if the origin splits into exactly two minimal Martin boundary points, one approached through each sector. This test is related to other integral tests due to Benedicks and Chevallier, the former in the special case of a Denjoy domain. We then generalise our test, replacing the pair of rays by an arbitrary number.
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[ Download ] [ 2017-01-08 20:35:39 uploaded by arkivadmin ] [ 755 downloads ] [ 0 comments ] [ Cited by 11 ] 
@inproceedings{michael1991martin,
  title={Martin boundaries of sectorial domains},
  author={Michael C. Cranston, and Thomas S. Salisbury},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203539235742591},
  booktitle={Arkiv for Matematik},
  volume={31},
  number={1},
  pages={27-49},
  year={1991},
}
Michael C. Cranston, and Thomas S. Salisbury. Martin boundaries of sectorial domains. 1991. Vol. 31. In Arkiv for Matematik. pp.27-49. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203539235742591.
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