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

Yuichi Shiozawa, Masayoshi Takeda

    Research output: Contribution to journalArticlepeer-review

    9 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 - Sept 1 2005

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

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