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Variations on a theorem by Edwards

Nilsson, Mårten LU and Wikström, Frank LU orcid (2025) In Arkiv for Matematik 63(2). p.391-405
Abstract

We discuss two variations of Edwards’ duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty common zero set. In the second variation, we replace suprema of point evaluations and infima over Jensen measures by suprema of other continuous functionals and infima over a set of measures defined through a natural order relation induced by the cone. As applications, we give some results on the propagation of discontinuities for Perron-Bremermann envelopes in hyperconvex domains as well as a characterization of minimal elements in the order relation mentioned above.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Arkiv for Matematik
volume
63
issue
2
pages
15 pages
publisher
International Press, Inc.
external identifiers
  • scopus:105024411542
ISSN
0004-2080
DOI
10.4310/ARKIV.2025.v63.n2.a9
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 by Institut Mittag-Leffler. All rights reserved.
id
91e5410a-e743-4988-88a2-b40ccbebcb37
date added to LUP
2026-02-23 15:48:26
date last changed
2026-02-23 15:49:08
@article{91e5410a-e743-4988-88a2-b40ccbebcb37,
  abstract     = {{<p>We discuss two variations of Edwards’ duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty common zero set. In the second variation, we replace suprema of point evaluations and infima over Jensen measures by suprema of other continuous functionals and infima over a set of measures defined through a natural order relation induced by the cone. As applications, we give some results on the propagation of discontinuities for Perron-Bremermann envelopes in hyperconvex domains as well as a characterization of minimal elements in the order relation mentioned above.</p>}},
  author       = {{Nilsson, Mårten and Wikström, Frank}},
  issn         = {{0004-2080}},
  language     = {{eng}},
  month        = {{10}},
  number       = {{2}},
  pages        = {{391--405}},
  publisher    = {{International Press, Inc.}},
  series       = {{Arkiv for Matematik}},
  title        = {{Variations on a theorem by Edwards}},
  url          = {{http://dx.doi.org/10.4310/ARKIV.2025.v63.n2.a9}},
  doi          = {{10.4310/ARKIV.2025.v63.n2.a9}},
  volume       = {{63}},
  year         = {{2025}},
}