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Dirichlet forms on unconstrained Sierpinski carpets
We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by...
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Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms
We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain...
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KMS Dirichlet forms, coercivity and superbounded Markovian semigroups on von Neumann algebras
We introduce a construction of Dirichlet forms on von Neumann algebras M associated to any eigenvalue of the Araki modular Hamiltonian of a faithful...
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An Averaging Principle for Stochastic Flows and Convergence of Non-Symmetric Dirichlet Forms
We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using...
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Ergodic decompositions of Dirichlet forms under order isomorphisms
We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a...
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Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances
This paper introduces an equivalent condition for the existence of regular local irreducible conservative Dirichlet forms that are self-similar under...
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Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms
We consider overdetermined problems for two classes of fully nonlinear equations with constant Dirichlet boundary conditions in a bounded domain in...
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Homogeneous Dirichlet Forms on p.c.f. Fractals and their Spectral Asymptotics
We formulate a class of “homogeneous” Dirichlet forms (DF) that aims to explore those forms that do not satisfy the conventional energy self-similar...
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Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications
We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique...
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On \(L^p\) Liouville Theorems for Dirichlet Forms
We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima’s ergodic theorem for the harmonic functions in...
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Littlewood-Paley-Stein estimates for non-local Dirichlet forms
We obtain the boundedness in L p spaces for all 1 < p < ∞ of the so-called vertical Littlewood-Paley functions for non-local Dirichlet forms in the...
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Energy Spaces, Dirichlet Forms and Capacities in a Nonlinear Setting
In this article we study lower semicontinuous, convex functionals on real Hilbert spaces. In the first part of the article we construct a Banach...
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Spectral Gap and Dirichlet Ground State
This chapter is entirely devoted to the studies of the lowest non-trivial eigenvalue of operators on graphs. For standard Laplacians on connected...