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


Generalized Watson transforms I: General theory

Author: Qifu Zheng
Journal: Proc. Amer. Math. Soc. 128 (2000), 2777-2787
MSC (2000): Primary 22E30, 43A32, 44A15; Secondary 43A65, 42A38
Published electronically: February 29, 2000
MathSciNet review: 1670364
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Abstract | References | Similar Articles | Additional Information


This paper introduces two main concepts, called a generalized Watson transform and a generalized skew-Watson transform, which extend the notion of a Watson transform from its classical setting in one variable to higher dimensional and noncommutative situations. Several construction theorems are proved which provide necessary and sufficient conditions for an operator on a Hilbert space to be a generalized Watson transform or a generalized skew-Watson transform. Later papers in this series will treat applications of the theory to infinite-dimensional representation theory and integral operators on higher dimensional spaces.

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

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  • 6. Q. Zheng, Generalized Watson transforms II: A new construction of complementary series of $GL(2, R)$ and properties of Bessel functions, in preparation.
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Additional Information

Qifu Zheng
Affiliation: Department of Mathematics and Statistics, The College of New Jersey, P.O. Box 7718, Ewing, New Jersey 08628-0718

PII: S 0002-9939(00)05399-5
Keywords: Unitary representations, intertwining operators, Watson transform, Hankel transform
Received by editor(s): October 5, 1998
Published electronically: February 29, 2000
Additional Notes: This research was partially supported by National Science Foundation grant DMS-9501191
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society

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