Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle
type: Item
instance of: scholarly article
title: Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle
zbMATH Open document ID: 1395.42067
author: Takayoshi Ogawa
author: Kento Seraku
published in: Communications on Pure and Applied Analysis
publication date: 2018-08-22T00:00:00Z
Mathematics Subject Classification ID: 42B37
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 6923392
zbMATH Keywords: logarithmic Sobolev inequality
zbMATH Keywords: Shannon's inequality
zbMATH Keywords: uncertainty principle
zbMATH Keywords: the best possible constants
MaRDI profile type: Publication
full work available at URL: cpaa.2018079
OpenAlex ID: W2796395469
cites work: Pitt's Inequality and the Uncertainty Principle
cites work: On Sharp Sobolev Embedding and The Logarithmic Sobolev Inequality
cites work: On a (\(\beta, q)\)-generalized Fisher information and inequalities involving \(q\)-Gaussian distributions
cites work: On generalized Cramér-Rao inequalities, generalized Fisher information and characterizations of generalized \(q\)-Gaussian distributions
cites work: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
cites work: The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
cites work: Logarithmic Sobolev Inequalities
cites work: Q3124805
cites work: Q4938929
cites work: Analysis.
cites work: Finite time blow up for a solution to system of the drift-diffusion equations in higher dimensions
cites work: Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
cites work: Minimum Value for c in the Sobolev Inequality $\| {\phi ^3 } \|\leqq c\| {\nabla \phi } \|^3 $
cites work: Uniqueness of ground states for quasilinear elliptic equations
cites work: A Mathematical Theory of Communication
cites work: Q5801644
cites work: Some inequalities satisfied by the quantities of information of Fisher and Shannon
cites work: Best constant in Sobolev inequality
cites work: Logarithmic Sobolev Inequalities for the Heat-Diffusion Semigroup
DOI: 10.3934/CPAA.2018079
description: scientific article; zbMATH DE number 6923392