Espaces de dirichlet: I. Le cas élémentaire

Sch’nol’s theorem for strongly local forms

“…Here we used the original condition from [9] that applies in the real and the complex case at the same time. Today, particularly in the real case, it is mostly expressed in an equivalent but formally weaker statement involving u ∨ 0 and u ∧ 1, see [16] Strong locality and the energy measure.…”

Operator Methods for Continuous-Time Markov Processes

“…More generally, Q does not have to be a finite measure. This approach to Markov processes was pioneered by Beurling and Deny (1958) and Fukushima (1971) for symmetric Markov processes. In this case both the operator A and the form f are symmetric.…”

“…We may now follow the approach of Beurling and Deny (1958) and Fukushima (1971) by constructing a Markov process associated with the form f 1 and the closed extension of f 2 . In what follows we will sketch only part of this construction.…”

Characterizations of Supports of Balayaged Measures

“…Beurling and Deny [1], [2] introduced Dirichlet spaces by generalizing the notion of "energy" in potential theory. They showed the existences of balayaged measures and condensor measures in the theory of Dirichlet spaces.…”