Localization operators and scalogram associated with the deformed Hankel wavelet transform (Q6042169)

It is known that the \((k, a\))-generalized wavelet transform in the case \(a = 1\) boils down to the \(k\)-Hankel wavelet transform, whereas for \(a = 2\) it reduces to the Dunkl-wavelet transform. The authors study the \(L_p\) boundedness and compactness of localization operators associated with the so-called deformed Hankel wavelet transform which corresponds to the case \(a =2/n\), \(n\in\mathbb{N}\). The spectral analysis of some typical examples of localization operators is given. Also, the scalogram associated with the deformed Hankel wavelet transform is introduced.