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Indices of Dirichlet forms


Author: Masanori Hino
Translated by: Masanori Hino
Journal: Sugaku Expositions 30 (2017), 187-205
MSC (2010): Primary 31C25; Secondary 60J60, 46G05, 58J60, 28A80, 60G44
DOI: https://doi.org/10.1090/suga/423
Published electronically: September 15, 2017
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Abstract: This article presents recent progress on the theory of Dirichlet forms, and, in particular, on the indices and related concepts of strong-local Dirichlet forms. We discuss the relation to geometric structures of the underlying spaces and local structures of the associated diffusion processes. Some results on quantitative estimates of indices for typical fractal sets are also explained.


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Additional Information

Masanori Hino
Affiliation: Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
Address at time of publication: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Email: hino@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/suga/423
Published electronically: September 15, 2017
Additional Notes: The author is a recipient of the 10th Analysis Prize (2011)
This research was partially supported by KAKENHI (24540170)
Article copyright: © Copyright 2017 American Mathematical Society