Displaying similar documents to “Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods”

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.

A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials

Szilárd Gy. Révész (2006)

Annales Polonici Mathematici

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We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed...

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.