Pluripotential theory associated with general bodies
Tom 130 / 2023
Annales Polonici Mathematici 130 (2023), 85-96
MSC: Primary 31C05; Secondary 31C10, 31C45, 32U05, 32U15, 32U35.
DOI: 10.4064/ap220608-4-1
Opublikowany online: 8 February 2023
Streszczenie
Pluripotential theory associated with a convex body $P\subset (\mathbb R^+)^d$ is a recently developing field of study. In this paper, motivated by work of J. J. Callaghan [Ann. Polon. Math. 90 (2007), 21–35] on $\theta $-incomplete polynomials in $\mathbb C^d$, we build the initial foundation of a pluripotential theory associated with more general bodies, specifically, when $P$ is the set-theoretic difference of two convex bodies $P_1, P_2$. We prove an approximation result for $P$-extremal functions and a global domination principle in this setting.
