Tuncay Tunç

Uniform and pointwise polynomial inequalities in regions with asymptotically conformal curve on weighted Bergman space

In this present work, we continue studying the Nikol’skii and Bernstein–Walsh type estimations for complex algebraic polynomials in the bounded and unbounded regions bounded by asymptotically conformal curve.

On the Asymptotic Behavior of p-Faber Polynomials for Domains with Piecewise Analytic Boundary

Let 𝐺⊂ℂ be a domain bounded by a piecewise analytic Jordans curve L, and let 𝐹𝑛,𝑝 denote the p-Faber polynomials associated with G. We derive estimates of the form 𝐹𝑛,𝑝(𝑧)=𝑂(1/𝑛𝜂), (𝑛→∞) for 𝑧∈𝐺, where 𝜂 depends on geometric properties of L and the parameter p. Also, we show that O cannot be replaced by o in the relation given above.