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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Resolution of singularities of convolutions
with the Gaussian kernel


Author: Kathrin Berkner
Journal: Proc. Amer. Math. Soc. 127 (1999), 425-435
MSC (1991): Primary 32S45; Secondary 44A35
MathSciNet review: 1468182
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Abstract | References | Similar Articles | Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04532-3
PII: S 0002-9939(99)04532-3
Keywords: Resolution of singularities, convolutions, bifurcations, orthogonal polynomials
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
Article copyright: © Copyright 1999 American Mathematical Society