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Proceedings of the American Mathematical Society

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



Hermite distributions
associated to the group $O(p,q)$

Author: Gerald B. Folland
Journal: Proc. Amer. Math. Soc. 126 (1998), 1751-1763
MSC (1991): Primary 33E30; Secondary 33C15, 35C05
MathSciNet review: 1451801
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Abstract | References | Similar Articles | Additional Information

Abstract: We calculate the tempered $O(p,q)$-invariant eigendistributions of the $O(p,q)$-invariant Hermite operator

\begin{equation*}-{\textstyle {\frac{1}{2}}}(\Delta _{x}- \Delta _{y}) +{\textstyle {\frac{1}{2}}}(|x|^{2}-|y|^{2})\qquad (x\in \mathbb{R}^{p},\ y\in \mathbb{R}^{q}).\end{equation*}

They are singular on the cone $|x|=|y|$ and are given elsewhere in terms of confluent hypergeometric functions.

References [Enhancements On Off] (What's this?)

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Additional Information

Gerald B. Folland
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350

Received by editor(s): December 5, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society