On the Extended Hardy Transformation of Generalized Functions

The classical Hardy transformation is extended to a certain class of generalized functions namely ultradistributions. The derivative of the extended Hardy transformation is obtained

An extension of

This paper investigates the L2 transform on a certain space of generalized functions. Two spaces of Boehmians have been constructed. The transform L2 is extended and some of its properties are also obtained

On q-analogues of the Mangontarum transform for certain q-Bessel functions and some application

AbstractSeveral q-analogues of certain integral transforms have been recently investigated by many authors in the recent past. In this paper, we introduce certain analogues of the so-called q-Mangontarum transform and implement the proposed variants to given classes of q-Bessel functions. The results of this paper are new and complement the previously known results of Mangontarum (2014). Some results related to q-Laplace transforms are also obtained

On a Widder potential transform and its extension to a space of locally integrable Boehmians

In this paper we investigate a Widder potential transform on certain spaces of Boehmians. We construct two spaces of Boehmians. One space of Boehmians is obtained by a well-known Mellin-type convolution product. The second space is obtained by another mapping acting with the first convolution. The extended Widder potential transform is therefore a mapping, that is, well-defined, linear, continuous, with respect to δ and Δ convergence, and consistent with the classical transform. Certain theorem is also established