Ergodic decomposition of Dirichlet forms via direct integrals and applications

Dello Schiavo L. 2021. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis.


Journal Article | Epub ahead of print | English

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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.
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Date Published
2021-10-06
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.
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Cite this

Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2021. doi:10.1007/s11118-021-09951-y
Dello Schiavo, L. (2021). 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, 2021. https://doi.org/10.1007/s11118-021-09951-y.
L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis. Springer Nature, 2021.
Dello Schiavo L. 2021. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis.
Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, Springer Nature, 2021, doi:10.1007/s11118-021-09951-y.
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arXiv 2003.01366

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