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

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- by Gerald B. Folland
- Proc. Amer. Math. Soc.
**126**(1998), 1751-1763 - DOI: https://doi.org/10.1090/S0002-9939-98-04331-7
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## 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

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## Bibliographic Information

**Gerald B. Folland**- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
- Email: folland@math.washington.edu
- Received by editor(s): December 5, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 1751-1763 - MSC (1991): Primary 33E30; Secondary 33C15, 35C05
- DOI: https://doi.org/10.1090/S0002-9939-98-04331-7
- MathSciNet review: 1451801