Uniform Positivity Improving Property, Sobolev Inequalities, and Spectral Gaps

Shigeki Aida

Research output: Contribution to journalArticlepeer-review

59 Citations (Scopus)

Abstract

We introduce a certain kind of strong ergodicity condition to study the existence of spectral gap for Markov generator. We can estimate the spectral gap using the ergodicity condition and a Sobolev type inequality. We apply our results to the Dirichlet form on Wiener spaces, Riemannian manifolds, and loop spaces.

Original languageEnglish
Pages (from-to)152-185
Number of pages34
JournalJournal of Functional Analysis
Volume158
Issue number1
DOIs
Publication statusPublished - 1998 Sep 10

ASJC Scopus subject areas

  • Analysis

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