Beckner type of the logarithmic Sobolev and a new type of Shannon’s inequalities and an application to the uncertainty principle

Kubo, Hideo; Ogawa, Takayoshi; Suguro, Takeshi

doi:10.1090/proc/14350

Beckner type of the logarithmic Sobolev and a new type of Shannon’s inequalities and an application to the uncertainty principle
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by Hideo Kubo, Takayoshi Ogawa and Takeshi Suguro

Proc. Amer. Math. Soc. 147 (2019), 1511-1518

DOI: https://doi.org/10.1090/proc/14350

Published electronically: December 19, 2018

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Abstract:

We consider the inequality which has a “dual” relation with Beckner’s logarithmic Sobolev inequality. By using the relative entropy, we identify the sharp constant and the extremal of this inequality. Moreover, we derive the logarithmic uncertainty principle like Beckner’s one.

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