This book contains an introductory and comprehensive account of the theory of (symmetric)
Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory …

The present book deals with the spectral geometry of infinite graphs. This topic involves the
interplay of three different subjects: geometry, the spectral theory of Laplacians and the heat …

The aim of this paper is to provide new characterizations of the curvature dimension
condition in the context of metric measure spaces $(X,\mathsf {d},\mathfrak {m}) $. On the …

We prove that the linear heat flow in a RCD (K,\infty) metric measure space (X, d, m) satisfies
a contraction property with respect to every L^ p-Kantorovich-Rubinstein-Wasserstein …

The Wiener process and the Poisson random measure are fundamental to the study of
stochastic processes; the former describes a continuous random evolution, and the latter …

The main theme of these lecture notes is to analyze heat conduction on disordered media
such as fractals and percolation clusters by means of both probabilistic and analytic …

We prove higher summability and regularity of Γ\big (f\big) Γ (f) for functions ff in spaces
satisfying the Bakry–Émery condition BE (K, ∞) BE (K,∞). As a byproduct, we obtain various …

For any p∈(1,∞) p∈(1,∞), we construct pp‐energies and the corresponding pp‐energy
measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self …

Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains
with prescribed conditions on the complement of the domain. Our main focus is on the …

This book deals with analytic treatments of Markov processes. Symmetric Dirichlet forms and
their associated Markov processes are important and powerful tools in the theory of Markov …