Bernstein Polynomial Inequality on a Compact Subset of the Real Line

2018/11/30 by В. В. Андриевскии, Andrievskii, Vladimir
Engineering · Mathematics · #30C85 #31A15 #41A17 #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1811.12863

openalex publication_date 2018/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove an analogue of the classical Bernstein polynomial inequality on a compact subset E of the real line. The Lipschitz continuity of the Green function for the complement of E with respect to the extended complex plane and the differentiability at a point of E of a special, associated with E, conformal mapping of the upper half-plane onto the comb domain play crucial role in our investigation.

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