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

Abstract

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, welldefined, linear, continuous, with respect to d and D convergence, and consistent with the classical transform. Certain theorem is also established. ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.