Abelian theorems for Laplace and Mehler-Fock transforms of generalized functions

The main purpose of this article is to exhibit Abelian theorems for the Laplace and the Mehler-Fock transforms of general order over distributions of compact support and over certain spaces of generalized functions.

Abelian theorems for fractional wavelet transform

In this paper, initial and final value Abelian theorems for fractional wavelet transform of function and tempered distributions are obtained. Using Mexican hat wavelet function, an application for Abelian theorems is investigated.

Final Value Abelian Theorems for the Stieltjes Transform of Generalized Functions

Limit results are obtained for the Stieltjes transform of generalized functions as the domain complex variable s approaches ∞ (final value results) in the right half plane. These results are of equivalent form as results for the transform as s approaches 0 (initial value results) in the right half plane.