Integral geometry, hypergroups, and I.M. Gelfand's question

Details Integral geometry, hypergroups, and I.M. Gelfand's question Integral geometry, hypergroups, and I.M. Gelfand's question

2011-06-25

arxiv.org/abs/1106.5159v1

Mathematics

Functional Analysis

10 pages, to be published in Doklady Mathematics, 2011

Scientific paper

This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are related to harmonic analysis on groups, but for other quite similar problems such relations are not clear? In the note we examine standard problems of integral geometry generating harmonic analysis (the Plancherel theorem etc.) on pairs of commutative hypergroups that are in a duality of Pontryagin's type. As a result new meaningful examples of hypergroups are constructed.

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