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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Bergman kernel function: Explicit formulas and zeroes
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by Harold P. Boas, Siqi Fu and Emil J. Straube PDF
Proc. Amer. Math. Soc. 127 (1999), 805-811 Request permission

Abstract:

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in $\mathbb {C}^3$ defined by the inequality $|z_1|+|z_2|+|z_3|<1$, have zeroes.
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Additional Information
  • Harold P. Boas
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
  • MR Author ID: 38310
  • ORCID: 0000-0002-5031-3414
  • Email: boas@math.tamu.edu
  • Siqi Fu
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
  • Address at time of publication: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071-3036
  • Email: sfu@math.tamu.edu
  • Emil J. Straube
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
  • MR Author ID: 168030
  • Email: straube@math.tamu.edu
  • Received by editor(s): June 30, 1997
  • Additional Notes: This research was supported in part by NSF grant number DMS 9500916.
  • Communicated by: Steven R. Bell
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 805-811
  • MSC (1991): Primary 32H10
  • DOI: https://doi.org/10.1090/S0002-9939-99-04570-0
  • MathSciNet review: 1469401