Convolution inequalities on finite cyclic groups and the pseudomeasure norm

Ritter, David L.

doi:10.1090/S0002-9939-1984-0746095-8

Convolution inequalities on finite cyclic groups and the pseudomeasure norm
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Proc. Amer. Math. Soc. 91 (1984), 589-592 Request permission

Abstract:

A characterization of the probability measures that define hypercontractive convolution operators on finite cyclic groups has been given in terms of the pseudomeasure norm. Here the pseudomeasure norm is shown to be a poor quantitative predictor of hypercontractiveness in an asymptotic sense.

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