collaborators

7 papers

math.FA2026

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…

math.AP2025

Caccioppoli-type inequalities for the Dunkl--Laplacian and their application to nonexistence result

Athulya P, Sandeep Kumar Verma

For a suitable function , we introduce the -Laplacian in the Dunkl framework as , where is th…

math.FA2025

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…

math.CA2025

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…

math.FA2025

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…

math.FA2025

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…