2023/09/22 by Mårten Nilsson, Frank Wikström, Nilsson, Mårten +1
Mathematics · #Analytic and geometric function theory #Functional Equations Stability Results #Holomorphic and Operator Theory #math.CV
paper · pdf · doi:10.48550/arxiv.2309.12762
openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 measures defined through a natural order relation induced by the cone. As applications, we give some results on propagation of discontinuities for Perron--Bremermann envelopes in hyperconvex domains as well as a characterization of minimal elements in the order relation mentioned above.