Tietze type extensions for absolutely continuous functions in the plane
Tom 285 / 2025
Studia Mathematica 285 (2025), 203-234
MSC: Primary 26B30; Secondary 47B40, 54C20
DOI: 10.4064/sm230808-29-10
Opublikowany online: 14 November 2025
Streszczenie
It is an open problem whether one can always extend an absolutely continuous function (in the sense of Ashton and Doust) on a compact subset of the plane to a larger compact set. We show that this can be done for a large family of initial domains whose components consist of polygons and convex curves. The connection between these extension theorems and the spectral theory of $AC(\sigma )$ operators is discussed.
