Perturbation of dirichlet forms and stability of fundamental solutions

Masaki Wada

研究成果: Article査読

4 被引用数 (Scopus)

抄録

Let {Xt}t≥0 be the α-stable-like or relativislic α-stable-like process on ℝd generated by a certain symmetric jump-type regular Dirichlet form (ε,F). It is known in [5,7] that the transition probability density p(t,x,y) of {Xt}t≥0 admits the two-sided estimates. Let μ be a positive smooth Radon measure in a certain class and consider the perturbed form εμ(u,u) = ε(u,u) - (u,u)μ. Denote by pμ(t,x,y) the fundamental solution associated with εμ. In this paper, we establish a necessary and sufficient condition on μ for pμ(t. x, y) having the same two-sided estimates as p(t, x, y) up to positive constants.

本文言語English
ページ(範囲)523-537
ページ数15
ジャーナルTohoku Mathematical Journal
66
DOI
出版ステータスPublished - 2014 12

ASJC Scopus subject areas

  • 数学 (全般)

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