L. P. Castro and M. M. Rodrigues

The Weierstrass-Whittaker Integral Transform

We introduce a Weierstrass type transform associated with the Whittaker integral transform, which we refer to as Weierstrass-Whittaker integral transform. We examine some properties of the transform and show, in particular, that it is helpful in solving of a generalized non-stationary heat equation with an initial condition.

Mathematics Subject Classification: 44A15, 33C15, 33C20, 33C90, 35A22, 35C15, 35K15

Key words and phrases: Weierstrass-Whittaker integral transform, Weierstrass transform, Whittaker integral transform, heat kernel, non-stationary heat type equation