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The Bergman kernel
for circular multiply connected domains
Moonja Jeong and Vladimir Mityushev |
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Vol. 233 (2007), No. 1, 145–157
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Abstract |
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The Bergman kernel is written in terms of a Poincaré series for every circular multiply connected domain in the plane. The proposed exact formula is based on the Green’s function constructed by Mityushev and S. V. Rogosin for multiply connected domains. First we verify the relation between the Green’s function and the Bergman kernel for unbounded domains. Then we apply it to construct the Bergman kernel. |
Keywords
Bergman kernel, Green’s function, harmonic measure,
multiply connected domain
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Mathematical Subject Classification 2000
Primary: 30C20, 30C40
Secondary: 20C35, 30E25
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Milestones
Received: 3 August 2006
Revised: 22 May 2007
Accepted: 22 October 2007
Published: 1 November 2007
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Authors |
| Moonja Jeong | |
| Department of Mathematics The University of Suwon Suwon P.O.Box 77 Kyungkido 440-600 Korea |
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| Vladimir Mityushev | |
| Department of Mathematics Pedagogical Academy ul. Podchorazych 2 Kraków 30-084 Poland |
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