4 papers · 1 filter
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…
Characterization of bi-parametric potentials and rate of convergence of truncated hypersingular integrals in the Dunkl setting
Sandeep Kumar Verma, Athulya P
In this work, we introduce the -semigroup for , which unifies and extends the classical Poisson (for ) and heat (for ) semigroups within the Dunkl analysis f…
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…