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Continuing earlier work, we investigate two related aspects of the set P(G) of continuous positive definite functions on a locally compact group G. The first one is the problem of when, for a closed subgroup H of G, every function in P(H) extends to some function in P(G). The second one is the question whether elements in G \ H can be separated from H by functions in P(G) which are identically one on H.

Extension and separation properties of positive definite functions on locally compact groups