1. Generalized Watson transforms I: General theory
- Author
-
Qifu Zheng
- Subjects
Hankel transform ,Series (mathematics) ,Watson ,Applied Mathematics ,General Mathematics ,Hilbert space ,Representation theory ,Noncommutative geometry ,Algebra ,symbols.namesake ,Operator (computer programming) ,Mathematics::Probability ,symbols ,Variable (mathematics) ,Mathematics - Abstract
This paper introduces two main concepts, called a generalized Watson transform and a generalized skewWatson 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.
- Published
- 2000