A Fractional Power for Dunkl Transforms in $L^{2}(\R^{N}, ω_{k}(x)dx)$

preprint2013arXivOpen access

A new fractional version of the Dunkl transform for real order $α$ is obtained. An integral representation, a Bochner type identity and a Master formula for this transform are derived.

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A Fractional Power for Dunkl Transforms in $L^{2}(\R^{N}, ω_{k}(x)dx)$

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A Fractional Power for Dunkl Transforms in L2(RN,ωk(x)dx) L^{2}(\R^{N}, ω_{k}(x)dx)L2(RN,ωk​(x)dx)

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A Fractional Power for Dunkl Transforms in $L^{2}(\R^{N}, ω_{k}(x)dx)$