Note: Please see pdf for full abstract with equations.
The aim of this paper is to introduce a translation operator associated to the generalized linear canonical Fourier Bessel transform Fmα,n and study some of the important properties, and we derive a convolution product for this transform and as application we study the heat equation and the heat semigroup related to the conjugate of the generalized Bessel operator Δmα,n.
MSC Classification: 33D15; 47A05; 47B90