On the radially deformed Fourier transform

2024/04/10 by De Bie, Hendrik, Yang, Ze
#30G35 #42A38 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.06839

Abstract

In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method from [4], we obtain the Laplace domain expressions of the kernel for the cases of m=2 and m > 2 when 1+c=(1)/(n), n∈ ℕ₀\backslash\1\ with n odd. Moreover, we show that the expressions can be simplified using the Poisson kernel and the generating function of the Gegenbauer polynomials. As a consequence, the inverse formulas are used to get the integral expressions of the kernel in terms of Mittag-Leffler functions.

Related

• The kernel of the generalized Clifford-Fourier transform and its generating function
• The kernel of the radially deformed Fourier transform
• A new construction of the Clifford-Fourier kernel
• On the Clifford-Fourier transform
• The class of Clifford-Fourier transforms