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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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Resolution of singularities of convolutions with the Gaussian kernel
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by Kathrin Berkner PDF
Proc. Amer. Math. Soc. 127 (1999), 425-435 Request permission

Abstract:

We present a complete classification of the zero set of a function which is a convolution with the Gaussian kernel. In the first part, we calculate the Taylor expansion of the convolution in a critical point. In the second part, we resolve the singularity with the help of the general Newton process which yields the Puiseux expansions for the solutions. Finally, we describe the resolved singularity in terms of Hermite polynomials.
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Additional Information
  • Kathrin Berkner
  • Affiliation: Department of Mathematics, Rice University, Houston, Texas 77251-1892
  • Email: berkner@cml.rice.edu
  • Received by editor(s): May 15, 1997
  • Additional Notes: Supported in part by Texas ATP under grant number TATP 003604-018 and by Alexander von Humboldt-Stiftung, Germany.
  • Communicated by: Frederick W. Gehring
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 425-435
  • MSC (1991): Primary 32S45; Secondary 44A35
  • DOI: https://doi.org/10.1090/S0002-9939-99-04532-3
  • MathSciNet review: 1468182