---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20814'
abstract:
- lang: eng
  text: 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.
acknowledgement: "Open Access funding enabled and organized by Projekt DEAL. The first
  three authors acknowledge financial support of the DFG within the priority programme
  Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic
  Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number
  F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC)
  under the European Union’s Horizon 2020 research and innovation programme (grant
  agreement No 716117)."
article_number: '6'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthias
  full_name: Keller, Matthias
  last_name: Keller
- first_name: Daniel
  full_name: Lenz, Daniel
  last_name: Lenz
- first_name: Marcel
  full_name: Schmidt, Marcel
  last_name: Schmidt
- first_name: Michael
  full_name: Schwarz, Michael
  last_name: Schwarz
- first_name: Melchior
  full_name: Wirth, Melchior
  id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
  last_name: Wirth
  orcid: 0000-0002-0519-4241
citation:
  ama: Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of
    intermediate forms between a regular Dirichlet form and its active main part.
    <i>Potential Analysis</i>. 2026;64(1). doi:<a href="https://doi.org/10.1007/s11118-025-10251-y">10.1007/s11118-025-10251-y</a>
  apa: Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2026). Boundary
    representations of intermediate forms between a regular Dirichlet form and its
    active main part. <i>Potential Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s11118-025-10251-y">https://doi.org/10.1007/s11118-025-10251-y</a>
  chicago: Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior
    Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet
    Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2026.
    <a href="https://doi.org/10.1007/s11118-025-10251-y">https://doi.org/10.1007/s11118-025-10251-y</a>.
  ieee: M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations
    of intermediate forms between a regular Dirichlet form and its active main part,”
    <i>Potential Analysis</i>, vol. 64, no. 1. Springer Nature, 2026.
  ista: Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2026. Boundary representations
    of intermediate forms between a regular Dirichlet form and its active main part.
    Potential Analysis. 64(1), 6.
  mla: Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between
    a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>,
    vol. 64, no. 1, 6, Springer Nature, 2026, doi:<a href="https://doi.org/10.1007/s11118-025-10251-y">10.1007/s11118-025-10251-y</a>.
  short: M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis
    64 (2026).
das_tickbox: '1'
dataavailabilitystatement: No datasets were generated or analysed during the current
  study.
date_created: 2025-12-14T23:02:03Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-07-27T10:25:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-025-10251-y
ec_funded: 1
external_id:
  arxiv:
  - '2301.01035'
file:
- access_level: open_access
  checksum: 9f5a4e900b8d4c74c6b5bf7c3bad54e1
  content_type: application/pdf
  creator: dernst
  date_created: 2026-07-27T10:25:21Z
  date_updated: 2026-07-27T10:25:21Z
  file_id: '22414'
  file_name: 2026_PotentialAnalysis_Keller.pdf
  file_size: 445935
  relation: main_file
  success: 1
file_date_updated: 2026-07-27T10:25:21Z
has_accepted_license: '1'
intvolume: '        64'
issue: '1'
keyword:
- Dirichlet forms
- Domination of semigroups
- Dirichlet
- Neumann and Robin boundary conditions
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
mathsc:
- 31C15
- 31C25
- 35A15
- 35J10
- 47D07
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
  grant_number: ESP156_N
  name: Gradient flow techniques for quantum Markov semigroups
publication: Potential Analysis
publication_identifier:
  eissn:
  - 1572-929X
  issn:
  - 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Boundary representations of intermediate forms between a regular Dirichlet
  form and its active main part
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2026'
...