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
[PDF]
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