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Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces

✍ Scribed by Yuzuru Inahama

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 286 KB
Volume: 179
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3677

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✦ Synopsis

In this paper we will prove the logarithmic Sobolev inequality on free loop groups for various heat kernel measures which P. Malliavin (1989Malliavin ( , 1991, in ``Diffusion Process and Related Problems in Analysis (M. A. Pinsley, Ed.), Vol. I, Birkha user, Basel) constructed. Those measures are associated with the Sobolev spaces of order s (s>1Â2) of the free loops in the Lie algebra. We will equipp the free loop groups with those metrics and will show that a formula of Weitzenbo ck type holds, which enables us to apply the method of Driver and Lohrenz (1996,

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✍ Shigeki Aida 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 294 KB

dedicated to professor norio shimakura on the occasion of his sixtieth birthday In this paper, we will give a sufficient condition on the logarithmic derivative of the heat kernel under which a logarithmic Sobolev inequality (LSI, in abbreviation) on a loop space holds. As an application, we prove