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arXiv · 2003.01366

Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications

Lorenzo Dello Schiavo
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Abstract

We study superpositions and 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, Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.

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Lorenzo Dello Schiavo. 2021-09-05. Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications. https://doi.org/10.1007/s11118-021-09951-y

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