A Mixed Parseval's Equation And a Generalized Hankel Transformation of Distributions

Abstract

Let an integral transform T﹛f﹜ of a complex valued function f(x) defined over the interval (0, ∞) be defined as One of the most usual procedures to extend the classical transform (l.a) to generalized functions consists in constructing a space A of testing functions over (0, ∞) which is closed with respect to the classical transform (l.a) and then the corresponding transform of the generalized function/ of the dual space of A is defined through This approach has been followed by L. Schwartz [13] and A. H. Zemanian [20], amongst others.