Article Sidebar
Published:
Nov 12, 2024Keywords:
Euclidean motion group, Gelfand pair, positive definite functions, spherical function, Bochner's theorem. 2020 AMS Subject Classification. 43A70, 43A90.
Article Details
Issue
Section
Articles
© Bachudo Science Co. Ltd. This work is licensed under the creative commons Attribution 4.0 International license.
Main Article Content
A Class Of Positive Definite Spherical Functions On The Euclidean Motion Groups
Abstract
Let be the Euclidean motion group realized as the semi-direct product of and . Let be a compact subgroup of . The set of positive definite spherical functions on is studied. Among other things, a result of Bochner which characterizes a K- bi-invariant positive definite spherical function in any locally compact group, is extended to the Gelfand pair ).
