Differential calculus on path and loop spaces II. Irreducibility of Dirichlet forms on loop spaces

Shigeki Aida

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We prove the irreducibility of a Dirichlet form on the based loop space on a compact Riemannian manifold. The Dirichlet form is defined by the gradient operator due to DRIVER and LÉANDRE. We also prove the uniqueness of the ground states of the Schrödinger operator for which the Dirichlet form satisfies the logarithmic Sobolev inequality. This is an extension of the corresponding results of GROSS ([28], [29]) to the case of general compact Riemannian manifolds.

Original languageEnglish
Pages (from-to)635-666
Number of pages32
JournalBulletin des Sciences Mathematiques
Volume122
Issue number8
DOIs
Publication statusPublished - 1998 Dec

ASJC Scopus subject areas

  • Mathematics(all)

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