Inversion of Generalized Flett Potentials Related to Wavelet-Like Transform

Abstract We obtained the explicit inversion formulas for the generalized Flett potentials with the wavelet-like transform generated by the generalized Poisson integrals (semigroups). These integrals are defined as the relevant generalized translation operator associated with the Laplace-Bessel differential operator. Moreover, in this article we proved some essential properties of the generalized Poisson integrals.