Year: 2024
Type: preprint
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 $1+c=\frac{1}{n}, n\in \mathbb{N}_0\backslash\{1\}$ 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.
Source: arXiv (Cornell University)
Authors: De Bie, Hendrik, Yang, Ze
Institution: Ghent University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: China Scholarship Council
Award: G8547083639
OpenAlex ID: W4394736711