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
OA 2023_PotentialAnalysis_DelloSchiavo.pdf 806.39 KB [Published Version]

Journal Article | Published | English

Scopus indexed
Department
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
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)
Access Level
OA Open Access
Date Uploaded
2023-10-04
MD5 Checksum
625526482be300ca7281c91c30d41725


Export

Marked Publications

Open Data ISTA Research Explorer

Web of Science

View record in Web of Science®

Sources

arXiv 2003.01366

Search this title in

Google Scholar