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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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A local geometric characterization of the Bochner-Martinelli kernel
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by Michael Bolt PDF
Proc. Amer. Math. Soc. 131 (2003), 1131-1136 Request permission

Abstract:

In this paper it is shown that a connected smooth local hypersurface in $\mathbb C^{n}$ for which the skew-hermitian part of the Bochner-Martinelli kernel has a weak singularity must lie on a surface having one of the following forms: $S^{2m+1} \!\times \mathbb C^{n-m-1}$ for some $1\leq m <n$, or $C\times \mathbb C^{n-1}$ where $C$ is a one-dimensional curve. This strengthens results of Boas about the Bochner-Martinelli kernel and it generalizes a result of Kerzman and Stein about the Cauchy kernel.
References
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Additional Information
  • Michael Bolt
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Email: mbolt@umich.edu
  • Received by editor(s): November 1, 2001
  • Published electronically: July 26, 2002
  • Communicated by: Mei-Chi Shaw
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1131-1136
  • MSC (2000): Primary 32A26; Secondary 53A07
  • DOI: https://doi.org/10.1090/S0002-9939-02-06699-6
  • MathSciNet review: 1948104