Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods

W. Pleśniak. "Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods." Banach Center Publications 72.1 (2006): 251-261. <http://eudml.org/doc/286336>.

@article{W2006,
abstract = {We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces of semialgebraic sets or other "small" subsets of ℝⁿ (ℂⁿ).},
author = {W. Pleśniak},
journal = {Banach Center Publications},
keywords = {multivariate Bernstein-Walsh and Markov type inequalities; Siciak and Zakharyuta extremal functions; approximation and extension of functions; algebraic sets; generalized Bernstein property},
language = {eng},
number = {1},
pages = {251-261},
title = {Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods},
url = {http://eudml.org/doc/286336},
volume = {72},
year = {2006},
}

TY - JOUR
AU - W. Pleśniak
TI - Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods
JO - Banach Center Publications
PY - 2006
VL - 72
IS - 1
SP - 251
EP - 261
AB - We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces of semialgebraic sets or other "small" subsets of ℝⁿ (ℂⁿ).
LA - eng
KW - multivariate Bernstein-Walsh and Markov type inequalities; Siciak and Zakharyuta extremal functions; approximation and extension of functions; algebraic sets; generalized Bernstein property
UR - http://eudml.org/doc/286336
ER -