Pointwise Bernstein-walsh-type Inequalities In Regions With Piecewise Dini-smooth Boundary

Year 2017, Volume: 5 Issue: 3, 35 - 47, 01.12.2017

P. Özkartepe

Abstract

In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Bergman space, where the contour and the weight functions have some singularities. In particular, we obtain pointwise Berstein-Walsh -type estimation for algebraic polynomials in the unbounded regions with piecewise Dini-smooth boundary having exterior zero angles

Keywords

Algebraic polynomials, Conformal mapping, Dini-smooth curve

Parçalı Dini-Düzgün Eğri ile Sınırlı Bölgelerde noktasal Bernstein-Walsh Tipi Eşitsizlikler

Abstract

Bu çalışmada, egri ve ağırlık fonksiyonlarının bazı tekilliklere sahip olduğu durumlarda, keyfi bir cebirsel polinomların modülünün büyüme hızını ağırlıklı Bergman uzayında inceliyoruz. Özellikle, parçalı Dini-düzgün dış sıfır açılara sahip olan sınırsız bölgelerde cebirsel polinomlar için noktasal Berstein-Walsh-tipi değerlendirmeler elde edilmiştir

Keywords

Cebirsel polinomlar, Konform dönüşüm, Dini-düzgün eğri

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