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Logarithmic Sobolev inequalities and hypercontractive estimates on the circle |
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| Authors: | Fred B Weissler |
| Affiliation: | Department of Mathematics, Brown University, Providence, Rhode Island 02912 U.S.A. |
| Abstract: | A logarithmic Sobolev inequality, analogous to Gross' inequality, is proved on the circle. From this inequality it follows that the Poisson and heat semigroups on the circle satisfy Nelson's hypercontractive estimates. |
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