Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity
Complex Variables
2026-01-21 v3
Abstract
We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with these Lelong classes are lower semicontinuous. These operators are given by integral, infimal, and supremal convolutions. Continuity properties of the logarithmic supporting function are studied and a precise description is given of when it is uniformly continuous. This gives a contradiction to published results about the H\"older continuity of these Siciak-Zakharyuta functions.
Cite
@article{arxiv.2410.20370,
title = {Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity},
author = {Bergur Snorrason},
journal= {arXiv preprint arXiv:2410.20370},
year = {2026}
}
Comments
16 pages. In v2: Moved an example out of the introduction, and other smaller fixes and clarifications