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 δδ and ΔΔ convergence, and consistent with the classical transform. Certain theorem is also established.