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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.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.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…