A Class Of Positive Definite Spherical Functions On The Euclidean Motion Groups

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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 ).