5 papers
Pseudo-differential operator associated with the linear canonical Dunkl transform
S. Umamaheswari, Sandeep Kumar Verma
In this paper, we introduce a pseudo-differential operator associated with the linear canonical Dunkl transform. For a particular class of symbols, we prove that this operator defi…
Wavelet-based inversion and analysis of Flett, Riesz and bi-parametric potentials in generalized Fourier framework
Athulya P, Umamaheswari S, Sandeep Kumar Verma
In this paper, we construct and analyze Bessel and Flett potentials associated with the heat and Poisson semigroups in the framework of the -generalized Fourier transform. W…
Uncertainty principles associated with the linear canonical Dunkl transform
Umamaheswari S, Sandeep Kumar Verma
In this paper, we establish analogs of Miyachi, Cowling-Price, and Heisenberg-Pauli-Weyl uncertainty principles in the framework of the linear canonical Dunkl transform. We also ob…
Calderon's reproducing formula and extremal functions associated with the linear canonical Dunkl wavelet transform
Sandeep Kumar Verma, Umamaheswari S
In this article, we undertake a two-fold investigation. First, we establish Calderons reproducing formula for the linear canonical Dunkl continuous wavelet transform. Further, we d…
Real Paley-Wiener theorems for the linear canonical Dunkl transform
Umamaheswari S, Sandeep Kumar Verma, Hatem Mejjaoli
We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we…