2011/06/25 by М. И. Граев, M. I. Graev, Graev, M. I. +2
Mathematics · Medicine · #43A10 #43A22 #43A62 #46F12 #46J25 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Representation Theory (math.RT) #math.FA #math.RT #msc:43A10 #msc:43A22 #msc:43A62 #msc:46F12 #msc:46J25
paper · pdf · doi:10.48550/arxiv.1106.5159
10 pages, to be published in Doklady Mathematics, 2011
arxiv created 2011/06/25 · openalex publication_date 2011/06/25 · arxiv updated 2011/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.