Boundary representations of intermediate forms between a regular Dirichlet form and its active main part

TL;DR

This paper characterizes all semigroups lying between a regular Dirichlet form's semigroup and its active main part, providing explicit descriptions in terms of boundary measures and open sets.

Contribution

It introduces a comprehensive characterization of intermediate semigroups between a Dirichlet form and its active part, with explicit boundary form descriptions for regular cases.

Findings

Explicit boundary measure descriptions for intermediate semigroups

Characterization of all semigroups between a Dirichlet form and its active part

Enhanced understanding of boundary representations in Dirichlet form theory

Abstract

We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary.