Displaying similar documents to “Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves”

Polynomial inequalities on algebraic sets

M. Baran, W. Pleśniak (2000)

Studia Mathematica

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We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in ℂ n (resp. ℝ n ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials 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...

On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

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Given integers D > 0 , n > 1 , 0 < r < n and a constant C > 0 , consider the space of r -tuples P → = ( P 1 ... P r ) of real polynomials in n variables of degree ≤ D , whose coefficients are ≤ C in absolute value, and satisfying det ∂ P i ∂ x i ( 0 ) 1 ≤ i , j ≤ r = 1 . We study the family { f | V } of algebraic functions, where f is a polynomial, and V = { | x | ≤ δ , P → ( x ) = 0 } , δ > 0 being a constant depending only on n , D , C . The main result is a quantitative extension theorem for these functions which is uniform in P → . This is used to prove Bernstein-type inequalities which are again uniform with respect to P → . ...