Proceedings of the American Mathematical Society

Author(s): Qifu Zheng
Journal: Proc. Amer. Math. Soc. 128 (2000), 2777-2787.
MSC (2000): Primary 22E30, 43A32, 44A15; Secondary 43A65, 42A38
Posted: February 29, 2000
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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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22E30, 43A32, 44A15, 43A65, 42A38

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

DOI: 10.1090/S0002-9939-00-05399-5
PII: S 0002-9939(00)05399-5
Keywords: Unitary representations, intertwining operators, Watson transform, Hankel transform
Received by editor(s): October 5, 1998
Posted: February 29, 2000
Additional Notes: This research was partially supported by National Science Foundation grant DMS-9501191
Communicated by: Roe Goodman
Copyright of article: Copyright 2000, American Mathematical Society

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