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Convolution inequalities on finite cyclic groups and the pseudomeasure norm

Author: David L. Ritter
Journal: Proc. Amer. Math. Soc. 91 (1984), 589-592
MSC: Primary 43A22; Secondary 43A75
MathSciNet review: 746095
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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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Article copyright: © Copyright 1984 American Mathematical Society