---
_id: '11916'
abstract:
- lang: eng
  text: A domain is called Kac regular for a quadratic form on L2 if every functions
    vanishing almost everywhere outside the domain can be approximated in form norm
    by functions with compact support in the domain. It is shown that this notion
    is stable under domination of quadratic forms. As applications measure perturbations
    of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and
    Schrödinger operators on manifolds are studied. Along the way a characterization
    of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally
    Riemannian metric measure spaces is obtained.
acknowledgement: "The author was supported by the German Academic Scholarship Foundation
  (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG)
  via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement
  during the author’s ongoing graduate studies and him as well as Marcel Schmidt for
  fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu
  and Peter Stollmann for valuable comments on a preliminary version of this article.
  He would also like to thank the organizers of the conference Analysis and Geometry
  on Graphs and Manifolds in Potsdam, where the initial motivation of this article
  was conceived, and the organizers of the intense activity period Metric Measure
  Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen
  access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '38'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
  full_name: Wirth, Melchior
  id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
  last_name: Wirth
  orcid: 0000-0002-0519-4241
citation:
  ama: Wirth M. Kac regularity and domination of quadratic forms. <i>Advances in Operator
    Theory</i>. 2022;7(3). doi:<a href="https://doi.org/10.1007/s43036-022-00199-w">10.1007/s43036-022-00199-w</a>
  apa: Wirth, M. (2022). Kac regularity and domination of quadratic forms. <i>Advances
    in Operator Theory</i>. Springer Nature. <a href="https://doi.org/10.1007/s43036-022-00199-w">https://doi.org/10.1007/s43036-022-00199-w</a>
  chicago: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances
    in Operator Theory</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s43036-022-00199-w">https://doi.org/10.1007/s43036-022-00199-w</a>.
  ieee: M. Wirth, “Kac regularity and domination of quadratic forms,” <i>Advances
    in Operator Theory</i>, vol. 7, no. 3. Springer Nature, 2022.
  ista: Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances
    in Operator Theory. 7(3), 38.
  mla: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances
    in Operator Theory</i>, vol. 7, no. 3, 38, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s43036-022-00199-w">10.1007/s43036-022-00199-w</a>.
  short: M. Wirth, Advances in Operator Theory 7 (2022).
date_created: 2022-08-18T07:22:24Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-02-21T10:08:07Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s43036-022-00199-w
file:
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  creator: dernst
  date_created: 2022-08-18T08:02:34Z
  date_updated: 2022-08-18T08:02:34Z
  file_id: '11921'
  file_name: 2022_AdvancesOperatorTheory_Wirth.pdf
  file_size: 389060
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file_date_updated: 2022-08-18T08:02:34Z
has_accepted_license: '1'
intvolume: '         7'
issue: '3'
keyword:
- Algebra and Number Theory
- Analysis
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Advances in Operator Theory
publication_identifier:
  eissn:
  - 2538-225X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Kac regularity and domination of quadratic forms
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: 7
year: '2022'
...