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arXiv · 2404.06839

On the radially deformed Fourier transform

Hendrik De Bie·Ze Yang
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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.

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Hendrik De Bie, Ze Yang. 2024-04-10. On the radially deformed Fourier transform. https://arxiv.org/abs/2404.06839

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