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

Yuichi Shiozawa, Masayoshi Takeda

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)135-151
ページ数17
ジャーナルPotential Analysis
23
2
DOI
出版ステータスPublished - 2005 9月 1

ASJC Scopus subject areas

  • 分析

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