Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 33E30, 33C15, 35C05

Retrieve articles in all journals with MSC (1991): 33E30, 33C15, 35C05


Additional Information

Gerald B. Folland
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Email: folland@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04331-7
PII: S 0002-9939(98)04331-7
Received by editor(s): December 5, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society