Pitt’s inequality and the uncertainty principle-Reference-Cited by-同舟云学术

Pitt’s inequality and the uncertainty principle

Published:1995 Issue:6 Volume:123 Page:1897-1905
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Beckner William

Abstract

The "uncertainty principle" is formulated using logarithmic estimates obtained from a sharp form of Pitt’s inequality. The qualitative nature of this result underlies the relations connecting entropy, the Hardy-Littlewood-Sobolev inequality, and the logarithmic Sobolev inequality.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1995-123-06/S0002-9939-1995-1254832-9/S0002-9939-1995-1254832-9.pdf

Reference18 articles.

1. Inequalities in Fourier analysis;Beckner, William;Ann. of Math. (2),1975

2. Sobolev inequalities, the Poisson semigroup, and analysis on the sphere 𝑆ⁿ;Beckner, William;Proc. Nat. Acad. Sci. U.S.A.,1992

3. A generalized Poincaré inequality for Gaussian measures;Beckner, William;Proc. Amer. Math. Soc.,1989

4. Annals of Mathematics Studies;Folland, Gerald B.,1989

5. Logarithmic Sobolev inequalities;Gross, Leonard;Amer. J. Math.,1975

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