Symmetric reflected diffusions
Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces.
The Definition of Energy in Non-Symmetric Translation Invariant Dirichlet Spaces.
The Dirichlet space: a survey.
The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms
The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
Topologies fines et compactifications associées à certains espaces de Dirichlet
Nous commençons par définir la notion d’espaces où est une capacité, ce qui permet d’introduire la notion de mesure d’énergie finie par rapport à , et de parler d’espaces de Dirichlet basés sur .Soit d’autre part un espace de Dirichlet en ce sens avec potentiels s.c.i. : on étudie les espaces de Dirichlet sur les ouverts fins correspondants à l’aide d’une compactification. On retrouve plus facilement et on généralise les résultats de D. Feyel et A. de La Pradelle, (Lecture Notes).
Transition density asymptotics for some diffusion processes with multi-fractal structures.
Transitions on a noncompact Cantor set and random walks on its defining tree
First, noncompact Cantor sets along with their defining trees are introduced as a natural generalization of -adic numbers. Secondly we construct a class of jump processes on a noncompact Cantor set from given pairs of eigenvalues and measures. At the same time, we have concrete expressions of the associated jump kernels and transition densities. Then we construct intrinsic metrics on noncompact Cantor set to obtain estimates of transition densities and jump kernels under some regularity conditions...
Upper bounds and conservativeness for semigroups associated with a class of Dirichlet forms generated by pseudo differential operators.
Variational fractals