Ergodic decomposition of Dirichlet forms via direct integrals and applications
Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.
Download
Journal Article
| Published
| English
Scopus indexed
Author
Department
Grant
Abstract
We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.
Publishing Year
Date Published
2023-03-01
Journal Title
Potential Analysis
Publisher
Springer Nature
Acknowledgement
The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.
Volume
58
Page
573-615
ISSN
eISSN
IST-REx-ID
Cite this
Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y
Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y
Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis. Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y.
L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023.
Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.
Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature, 2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
Main File(s)
File Name
2023_PotentialAnalysis_DelloSchiavo.pdf
806.39 KB
Access Level
Open Access
Date Uploaded
2023-10-04
MD5 Checksum
625526482be300ca7281c91c30d41725
Export
Marked PublicationsOpen Data ISTA Research Explorer
Web of Science
View record in Web of Science®Sources
arXiv 2003.01366
Google Scholar