Variational formula for dirichlet forms and estimates of principal eigenvalues for symmetric α-stable processes

Yuichi Shiozawa, Masayoshi Takeda

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, we prove a variational formula for Dirichlet forms generated by general symmetric Markov processes. As its applications, we obtain lower bound estimates of the bottom of spectrum for symmetric Markov processes. Moreover, for a positive measure μ charging no set of zero capacity, we give a new proof of an L 2(μ)-estimate of functions in Dirichlet spaces. Finally, we calculate the principal eigenvalues for absorbing and time changed α-stable processes and obtain conditions for some measures being gaugeable.

Original languageEnglish
Pages (from-to)135-151
Number of pages17
JournalPotential Analysis
Volume23
Issue number2
DOIs
Publication statusPublished - Sep 1 2005

Keywords

  • Dirichlet form
  • Principal eigenvalue
  • Symmetric α-stable process
  • Time change
  • Variational formula

ASJC Scopus subject areas

  • Analysis

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