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

Hideo Kubo; Takayoshi Ogawa; Takeshi Suguro

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

Hideo Kubo, Takayoshi Ogawa, Takeshi Suguro

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1511-1518
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	4
DOIs	https://doi.org/10.1090/proc/14350
Publication status	Published - 2018

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "Beckner type of the logarithmic sobolev and a new type of shannon{\textquoteright}s inequalities and an application to the uncertainty principle",

abstract = "We consider the inequality which has a “dual” relation with Beckner{\textquoteright}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{\textquoteright}s one.",

author = "Hideo Kubo and Takayoshi Ogawa and Takeshi Suguro",

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AU - Kubo, Hideo

AU - Ogawa, Takayoshi

AU - Suguro, Takeshi

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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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U2 - 10.1090/proc/14350

DO - 10.1090/proc/14350

M3 - Article

AN - SCOPUS:85062005133

SN - 0002-9939

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SP - 1511

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

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

Abstract

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