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Real Paley–Wiener theorems for the ( k , a )‐generalized Fourier transform
Author(s) -
Li Shanshan,
Leng Jinsong,
Fei Minggang
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6449
Subject(s) - mathematics , fourier transform , fourier inversion theorem , pure mathematics , generalization , fractional fourier transform , unitary state , multiplicity (mathematics) , algebra over a field , generalized function , mathematical analysis , fourier analysis , political science , law
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 onR d ∖ { 0 } and a >0 arises from the interpolation of the two Lie algebra s l ( 2 , R ) actions on the Weil representation of Mp ( d , R ) and the minimal unitary representation of the O ( d +1,2).