Domination of semigroups generated by regular forms

TL;DR

This paper characterizes when one $C_0$-semigroup dominates another using regular forms and explores how positivity relates to the locality of these forms, providing a theoretical framework for understanding domination in semigroup theory.

Contribution

It introduces a representation for regular forms associated with dominated $C_0$-semigroups and establishes a link between positivity and form locality.

Findings

Representation for regular forms in dominated semigroups

Characterization of domination via regular forms

Relationship between positivity and form locality

Abstract

We give a representation for regular forms associated with dominated $C_0$-semigroups which, in turn, characterises domination of $C_0$-semigroups associated with regular forms. In addition, we prove a relationship between the positivity of (dominated) $C_0$-semigroups and the locality of the associated forms.