Geodesic
On Positive Definite Functions over a Locally Compact Group
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 892-896

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we are concerned with several questions on positive definite functions over a Hausdorff locally compact group. The main result, Theorem A, gives some necessary and sufficient conditions for to be a positive definite function when μ is a (complex Radon) measure. In particular, is a positive definite function if and only if μ ∊ L 2, and Theorem B then follows by giving a complete characterization of functions of the type , where f ∊ L 2. Perhaps the most interesting aspect of these results is that they provide further examples of results over a non-abelian, non-compact group, which otherwise are simple consequences (with μ, a bounded measure in Theorem A) of the theorems of Plancherel and Bochner.Unless otherwise specified, all notation and definitions will follow [1;2]. The underlying group will always be G, a Hausdorff locally compact group with identity e, and with left Haar measure dx. 
Price, J. F. On Positive Definite Functions over a Locally Compact Group. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 892-896. doi: 10.4153/CJM-1970-102-2
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