Displaying similar documents to “Polynomial inequalities on algebraic sets”

Bernstein classes

N. Roytwarf, Yosef Yomdin (1997)

Annales de l'institut Fourier

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One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes R . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one...

Markov inequality on sets with polynomial parametrization

Mirosław Baran (1994)

Annales Polonici Mathematici

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The main result of this paper is the following: if a compact subset E of ℝ n is UPC in the direction of a vector v ∈ S n - 1 then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].

Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods

W. Pleśniak (2006)

Banach Center Publications

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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...

Polynomial inequalities in Banach spaces

Mirosław Baran (2015)

Banach Center Publications

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We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.

Siciak's extremal function in complex and real analysis

W. Pleśniak (2003)

Annales Polonici Mathematici

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The Siciak extremal function establishes an important link between polynomial approximation in several variables and pluripotential theory. This yields its numerous applications in complex and real analysis. Some of them can be found on a rich list drawn up by Klimek in his well-known monograph "Pluripotential Theory". The purpose of this paper is to supplement it by applications in constructive function theory.

On the dynamics of extendable polynomial endomorphisms of ℝ²

Ewa Ligocka (2007)

Annales Polonici Mathematici

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We extend the results obtained in our previous paper, concerning quasiregular polynomials of algebraic degree two, to the case of polynomial endomorphisms of ℝ² whose algebraic degree is equal to their topological degree. We also deal with some other classes of polynomial endomorphisms extendable to ℂℙ².