Bulletin of the
Korean Mathematical Society BKMS

Given a compact subset $P \subset (\mathbb R^+)^d$ and a compact set $K$ in $\mathbb C^d$. We concern with the Bernstein-Markov properties of the triple $(P,K,\mu)$ where $\mu$ is a finite positive Borel measure with compact support $K$. Our approach uses (global) $P$-extremal functions which is inspired by the classical case (when $P=\Sigma$ the unit simplex) in [7].

Keywords: Plurisubharmonic functions, Bernstein-Markov property, body convex

MSC numbers: Primary 31B15, 32U35, 32U15

Supported by: This work was financially supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant Number 101.02-2019.304. This work was started while the authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM) in the Winter of 2019. We would like to thank VIASM for its financial support and hospitality. The first named author was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant Number 101.02-2019.304.