LOGARITHMIC SOBOLEV INEQUALITY FOR $H_0^s$-METRIC ON PINNED LOOP GROUPS-Reference-Cited by-同舟云学术

LOGARITHMIC SOBOLEV INEQUALITY FOR $H_0^s$-METRIC ON PINNED LOOP GROUPS

Published:2004-03 Issue:01 Volume:07 Page:1-26
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

INAHAMA YUZURU¹

Affiliation:

1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Abstract

In this paper we prove the logarithmic Sobolev inequality on pinned loop groups over compact Lie groups equipped with [Formula: see text]-metric (s>1/2). We also compute the Ricci tensor with respect to [Formula: see text]-metric and investigate its asymptotic behavior as s decreases to 1/2.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025704001505

Reference9 articles.

1. Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces

2. A logarithmic Sobolev inequality for the free loop group

3. Logarithmic Sobolev Inequalities for Pinned Loop Groups

4. Integration by Parts Formula and Logarithmic Sobolev Inequality on the Path Space Over Loop Groups

5. Integration by parts for heat measures over loop groups

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