Mosco Convergence of Stable-Like Non-Local Dirichlet Forms on Metric Measure Spaces

Abstract

We prove that stable-like non-local Dirichlet forms converge to local Dirichlet form in the sense of Mosco on metric measure spaces. We prove that subordinated Dirichlet forms converge to the original Dirichlet form in the sense of Mosco on metric measure spaces.

13 pages. The main result Theorem 1.3 was already obtained in Lemma 4.2 of Z.-Q. Chen and R. Song, Continuity of eigenvalues of subordinate processes in domains. Math. Z. 252 (2006), 71-89. Some other results were moved to arXiv:1912.09868