Constructing Fourier Transforms on the Quantum E(2)-Group

被引：0
作者：
Jeroen Noels
机构：
[1] Katholieke Universiteit Leuven,Department wiskunde
来源：
Algebras and Representation Theory | 2004年 / 7卷
关键词：
quantum group; quantum plane; Euclidean motions; Fourier transform; group duality; -Bessel function; -Hankel transform; -moment problem; Plancherel formula;
D O I：
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学科分类号：
摘要：
In a previous article we proposed an algebraic setting in which to perform harmonic analysis on noncompact, nondiscrete quantum groups and in particular, on quantum E(2). In the present paper we shall explicitly construct Fourier transforms between quantum E(2) and its Pontryagin dual, involving Hahn—Exton q-Bessel functions as kernel, prove Plancherel and inversion formulas, etc. We also develop a theory of q-Hankel transformation of entire functions, based on the definition proposed by Koornwinder and Swarttouw.
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页码：101 / 138
页数：37
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