\((k,a)\)-generalized wavelet transform and applications (Q2174849)

The author introduces the notion of a \((k,a)\)-generalized wavelet transform, based on the \((k,a)\)-generalized Fourier transform. Particular cases are the classical and the Dunkl wavelet transforms. The restriction of the \((k,a)\)-generalized wavelet transform to radial functions is given by the generalized Hankel wavelet transform. He proves for this new transform Plancherel's formula, an inversion theorem, and a Calderón reproducing formula, and studies generalized wavelet localization operators. An application to Tikhonov regularization on generalized Sobolev spaces is given.