Logarithm Sobolev and Shannon’s Inequalities Associated with the Deformed Fourier Transform and Applications

Logarithm Sobolev and Shannon’s Inequalities Associated with the Deformed Fourier Transform and Applications

By using the symmetry of the Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and a logarithmic Sobolev inequality for the Dunkl transform. Combining these inequalities, we obtain a new, short proof for Heisenberg-type uncertainty principles in the Dunkl setting. Moreover, by combi...

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Bibliographic Details
Main Authors: Saifallah Ghobber, Hatem Mejjaoli
Format: Article
Language:English
Published: MDPI AG 2022-06-01
Series:Symmetry
Subjects:
Sobolev inequality
Shannon inequality
logarithmic Sobolev inequality
Dunkl transform
uncertainty principle
Online Access:https://www.mdpi.com/2073-8994/14/7/1311

Internet

https://www.mdpi.com/2073-8994/14/7/1311

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