About Some Random Fourier Series and Multipliers Theorems on Compact Commutative Hypergroups
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The character theory of compact commutative hypergroups is yet far from being well understood; as this paper shows, the behaviour of the Plancherel measure is related to some deeper harmonic analysis involving notably Sidon sets. Pioneering work related to this area has been performed a long time ago by R. Vrem, K. Ross, J. Fournier (see references below). This elementary study provides only a sample of easy results, but paves the way to apparently much deeper questions.
This paper is comprised of two parts: the first one has been already mentioned; the second provides some easy multiplier theorems. In the context of hypergroups, and despite its elementary character, much of the material presented here is new.
KeywordsApproximate Identity Multiplier Theorem Classical Line Plancherel Measure Bounded Approximate Identity
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