Polynomial inequalities on certain algebraic hypersurfaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Bialas-Ciez, Leokadia¹  Calvi, Jean-Paul^2,3  Kowalska, Agnieszka⁴ 

[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Univ Toulouse III, Inst Math, F-31062 Toulouse 9, France

[3] CNRS, UMR 5219, F-31062 Toulouse 9, France

[4] Pedag Univ, Inst Math, Podchorazych 2, PL-30084 Krakow, Poland

关键词: Markov inequality;    Schur inequality;    Division inequality;    Algebraic hypersurfaces;   

DOI  :  10.1016/j.jmaa.2017.11.010

来源: Elsevier

【 摘 要 】

We prove that any Markov set in C-N satisfies a Schur type inequality for polynomials and we give a generalization for polynomial matrices. As a consequence, we obtain polynomial inequalities on compact subsets of algebraic hypersurfaces of the form V = {z(N+1)(k), = s(z(1),..., z(N))} subset of CN+1, where s is a non constant polynomial of N variables. We also give a condition equivalent to the Markov inequality on compact subsets of V. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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