Some generalizations of Bessel and Flett potentials associated to the Laplace–Bessel differential operator

Abstract

ABSTRACTWe introduce the notion of bi-parametric potential-type operators, which generalize the Bessel and Flett potentials associated to singular Laplace–Bessel differential operator. Explicit inversion formulas for them are obtained by using a special wavelet-like transform, generated by the so-called ‘modified beta-semigroup’.