Mean periodic functions
In Section 4.1 we have seen that the study of varieties in C(G) is equivalent to the study of solution spaces of convolution type functional equations. As the solutions of convolution type functional equations are mean periodic functions, it seems to be reasonable to set them into the center of our investigations. We recall (see also ) that for a locally compact Abelian group G the continuous function f : G → ℂ is called mean periodic if there exists a nonzero compactly supported complex Radon measure μ on G such that
KeywordsPeriodic Function Nonnegative Integer Topological Vector Space Compact Abelian Group Spectral Synthesis
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