Real Paley–Wiener theorems for the ( k , a )‐generalized Fourier transform
Shanshan Li, Jinsong Leng, Minggang Fei
Source abstract
In this paper, we obtain several versions of the real Paley–Wiener theorems for the ( k , a )‐generalized Fourier transform recently investigated at length by Ben Saïd, Kobayashi, and Ørsted. This generalized Fourier transform can be regarded as a two‐parameter generalization of Howe's description of classical Fourier transform, where k is a multiplicity function for the Dunkl operators on and a >0 arises from the interpolation of the two Lie algebra actions on the Weil representation of and the minimal unitary representation of the O ( d +1,2).
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