A STUDY ON BI-PARAMETRIC POTENTIALS: INVERSION FORMULAS UTILIZING WAVELET-LIKE TRANSFORMATIONS IN WEIGHTED LEBESGUE SPACES

A STUDY ON BI-PARAMETRIC POTENTIALS: INVERSION FORMULAS UTILIZING WAVELET-LIKE TRANSFORMATIONS IN WEIGHTED LEBESGUE SPACES

G. Yıldız, R. Kahraman, S. Bayrakçı

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Abstract

We introduce a new family of wavelet-like transforms based on bi-parametric semigroups associated with the Laplace-Bessel differential operator. Using these transforms, we obtain new inversion formulas for bi-parametric potentials in the framework of weighted Lebesgue spaces.

Keywords

Wavelet transforms, Abel-Poisson semigroup, Gauss-Weierstrass semigroup, inversion formulas, Bessel potentials, Modified Bessel potentials