Boundary Representations of Intermediate forms between a Regular Dirichlet form and its Active Main Part

Matthias Keller; Daniel Lenz; Marcel Schmidt; Michael Schwarz; Melchior Wirth

doi:10.1007/s11118-025-10251-y

December 3, 2025Potential AnalysisOpen Access

Boundary Representations of Intermediate forms between a Regular Dirichlet form and its Active Main Part

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Key Points

Quadratic forms of semigroups are described explicitly in terms of pairs involving open sets and measures.
The findings connect the structure of Dirichlet forms to their active main parts, offering a deeper understanding.
Analysis focused on sandwiched semigroups clarifies their properties in the context of regular Dirichlet forms.
Implications may extend to various mathematical modeling scenarios where boundary behaviors are significant.

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Implication

Analysis reveals characteristics of semigroups linked to Dirichlet forms, indicating potential applications in mathematical modeling.

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.

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Keller et al. (2025) studied this question.

synapsesocial.com/papers/693231308e51979591dce852 https://doi.org/10.1007/s11118-025-10251-y

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Boundary Representations of Intermediate forms between a Regular Dirichlet form and its Active Main Part

Key Points

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Implication

Abstract

Discussion

Cite This Study

Boundary Representations of Intermediate forms between a Regular Dirichlet form and its Active Main Part

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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