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 F m ν 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 ∆ m ν .

WITHDRAWN: Generalized translation operator and Heat equation for the generalized canonical Fourier Bessel transform

“…x associated with the Bessel operator ∆ m α . Ghazouani [8] defined the generalized translation operator T α,m x associated with ∆ m α by : T α,m x f (y) = u(x, y), where u(x, y) is the unique solution of the problem :…”

“…Let m ∈ SL(2, R) such that b ̸ = 0 and let f and g be measurable functions on [0; +∞[. Ghazouani [8] defined the convolution of f and g by :…”

“…In the present work, we continue the analysis begun in [1] by studying the generalized translation operator and the generalized convolution product related to this transformation. Following the framework of Al Subaie and Mourou [2] and [8], we introduce a generalized translation operator T α,m…”