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arXiv · 2202.05013

Equality in Hausdorff-Young for Hypergroups

Choiti Bandyopadhyay·Parasar Mohanty
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Abstract

It has been shown in "On the Hausdorff-Young theorem for commutative hypergroups" by Sina Degenfeld-Schonburg, that one can extend the domain of Fourier transform of a commutative hypergroup $K$ to $L^p(K)$ for $1\leq p \leq 2$, and the Hausdorff-Young inequality holds true for these cases. In this article, we examine the structure of non-zero functions in $L^p(K)$ for which equality is attained in the Hausdorff-Young inequality, for $1<p<2$, and further provide a characterization for the basic uncertainty principle for commutative hypergroups with non-trivial centre.

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Choiti Bandyopadhyay, Parasar Mohanty. 2022-02-10. Equality in Hausdorff-Young for Hypergroups. https://doi.org/10.1007/s43037-022-00211-8

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