Equality in Hausdorff-Young for Hypergroups
Choiti Bandyopadhyay, Parasar Mohanty

TL;DR
This paper investigates the conditions under which equality holds in the Hausdorff-Young inequality for Fourier transforms on commutative hypergroups, extending classical results and exploring uncertainty principles.
Contribution
It characterizes functions attaining equality in the Hausdorff-Young inequality and analyzes the basic uncertainty principle on commutative hypergroups with non-trivial centers.
Findings
Characterization of functions achieving equality in Hausdorff-Young inequality.
Extension of Fourier transform domain to $L^p(K)$ for $1 \\leq p \\leq 2$.
Analysis of uncertainty principles on hypergroups.
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 to for , and the Hausdorff-Young inequality holds true for these cases. In this article, we examine the structure of non-zero functions in for which equality is attained in the Hausdorff-Young inequality, for , and further provide a characterization for the basic uncertainty principle for commutative hypergroups with non-trivial centre.
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