Polynomial approximation and twenty years later.
Polynomial inequalities in Banach spaces
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.
Polynomial inequalities on algebraic sets
We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in (resp. ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.
Polynomial inequalities on general subsets of
Problème de Bernstein pour les fonctions différentiables
Properties of some bivariate approximants.
The smoothness and approximation properties of certain discrete operators for bivariate functions are examined.
Properties of the modulus of continuity for monotonous convex functions and applications.