Bulletin of the
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Bull. Korean Math. Soc. 2022; 59(4): 811-825

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210341

Copyright © The Korean Mathematical Society.

$P$-extremal functions and Bernstein-Markov properties associated to compact sets in $\mathbb R^d$

Hoang Thieu Anh, Kieu Phuong Chi, Nguyen Quang Dieu, Tang Van Long

Hanoi; Saigon University; Hanoi; Hanoi

Abstract

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 \cite{BloomLe99}.

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

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

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