Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on \(\mathbb{R}^d \times \mathbb{R}_{+}\)
The authors describe some properties of the Dunkl-Bessel-Laplace operator \(\Delta_{k,\beta}\) which is a special partial differential-difference operator. Corresponding to \(\Delta_{k,\beta}\), a translation operator and a convolution is introduced. For the Dunkl-Bessel transform, an inversion formula and a Plancherel-type theorem are presented. Associated with \(\Delta_{k,\beta}\), Gaussian wavelets are constructed.
partial differential-difference operator
scientific article; zbMATH DE number 6510995
scientific article