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Decomposition of positive definite functions defined on a neighbourhood of the identity. (English) Zbl 0626.43006
Let V be a symmetric open neighbourhood of the identity of a topological group G. We show that every positive definite function f on v can be written as $$f=f_ c+f_ s$$ where $$f_ c$$ and $$f_ s$$ are positive definite functions on V, $$f_ c$$ is continuous and $$f_ s$$ averages to zero. If G is locally compact with Haar measure $$m_ G$$ and f is $$m_ G$$-measurable then $$f_ s=0$$, $$m_ G$$-almost everywhere.

##### MSC:
 43A35 Positive definite functions on groups, semigroups, etc.
##### Keywords:
topological group; positive definite function; Haar measure
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##### References:
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