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arXiv · 1304.2880

Dunkl positive definite functions

Jamel El Kamel·Khaled Mehrez
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Abstract

We introduce the notion of Dunkl positive definite and strictly positive definite functions on $\mathbb{R}^{d}$. This done by the use of the properties of Dunkl translation. We establish the analogue of Bochner's theorem in Dunkl setting. The case of radial functions is considered. We give a sufficient condition for a function to be Dunkl strictly positive definite on $\mathbb{R}^{d}.$

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Jamel El Kamel, Khaled Mehrez. 2013-04-10. Dunkl positive definite functions. https://arxiv.org/abs/1304.2880

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