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Generalized Watson Transforms I: General Theory

Qifu Zheng
Proceedings of the American Mathematical Society
Vol. 128, No. 9 (Sep., 2000), pp. 2777-2787
Stable URL: http://www.jstor.org/stable/119881
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Generalized Watson Transforms I: General Theory
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Abstract

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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