Constructing Fourier Transforms on the Quantum E(2)-Group
by Noels, Jeroen
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.
DOI: 10.1023/B:ALGE.0000026845.01180.1d
Print publication date: 5/1/2004
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