This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Kraus, Christiane2016-03-242019-06-2820060946-8633https://doi.org/10.34657/2651https://oa.tib.eu/renate/handle/123456789/2155In this paper we extend the theory of maximal convergence introduced by Walsh to functions of squared modulus holomorphic type. We introduce in accordance to the well-known complex maximal convergence number for holomorphic functions a real maximal convergence number for functions of squared modulus holomorphic type and prove several maximal convergence theorems. We achieve that the real maximal convergence number for F is always greater or equal than the complex maximal convergence number for g and equality occurs if L is a closed disk in R^2. Among other various applications of the resulting approximation estimates we show that for functions F of squared holomorphic type which have no zeros in a closed disk B_r the relation limsupntoinftysqrt[n]En(Br,F)=limsupntoinftysqrt[n]En(partialBr,F) is valid, where E_n is the polynomial approximation error.application/pdfeng510Polynomial approximation in 2–spaceMaximal convergenceBernstein-Walsh’s type theoremsreal-analytic functionsReport