On a widder potential transform and its extension to a space of locally integrable boehmians

Abstract EN

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.