Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 280
The Logarithmic Sobolev Inequality on the circle Z/2πZ
M'Hammed Ouyahia, Ali Hafidi and Moulay Rchid Sidi Ammi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 29, 2022
March 03, 2243
April 15, 2243

Abstract: In this work, we introduce the basic notions of the hypercontractivity property of semigroups and functionals inequalities (Sobolev inequality, logarithmic Sobolev inequality, and the spectral gap inequality). We will focus the study on the characteristics and property of the logarithmic Sobolev inequality for the uniform measure on the circle Z/2πZ, by using the heat semigroup technics and integration by parts. It is note worthy that the previous inequality proved by Weissler [5], by virtue of a complicated calculation and also by Rothaus [3] by a variational method.