Generalized translation operator and the Heat equation for the canonical Fourier Bessel transform

Abstract

The aim of this paper is to introduce a translation operator associated to the canonical Fourier Bessel transform ${\mathcal{F}}_{\nu }^{\mathbf{m}}$ and study some of the important properties. We derive a convolution product for this transform and as application we study the heat equation and the heat semigroup related to ${\Delta }_{\nu }^{\mathbf{m}}.$