Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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P-EXTREMAL FUNCTIONS AND BERNSTEIN-MARKOV PROPERTIES ASSOCIATED TO COMPACT SETS IN ℝd

  • Anh, Hoang Thieu (University of Transport and Communications) ;
  • Chi, Kieu Phuong (Department of Mathematics and Applications Saigon University) ;
  • Dieu, Nguyen Quang (Department of Mathematics Hanoi National University of Education and Thang Long Institute of Mathematics and Applied Sciences) ;
  • Long, Tang Van (Department of Mathematics Hanoi National University of Education)
  • Received : 2021.04.25
  • Accepted : 2022.05.26
  • Published : 2022.07.31
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Abstract

Given a compact subset P ⊂ (ℝ+)d and a compact set K in ℂd. We concern with the Bernstein-Markov properties of the triple (P, K, 𝜇) where 𝜇 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 = Σ the unit simplex) in [7].

Keywords

Acknowledgement

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.

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