Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods

• Autorzy: W. Pleśniak
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 32B20: Semi-analytic sets and subanalytic sets
• 14P05: Real algebraic sets
• 32U35: Pluricomplex Green functions
• 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 72
• Numer: 1
• Strony: 251-261

Daty

wydano

2006

Twórcy

autor

W. Pleśniak

• Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/bc72-0-16