Let μ be a finite complex Borel measure supported on the unit circle.In this paper, we are concerned with the characterization of the sets of functions satisfying the generalized mean value equation of the form.and for all ξ ∈ , | ξ | = R for some fixed R > 0.
ABSTRACT.We provide new proofs of the theorems of Choquet and Deny and of Foguel concerning iterates of convolutions of a measure on a locally compact abelian group.
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