Boundedness of derivatives and anti-derivatives of holomorphic functions as a rare phenomenon

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Siskaki, Maria¹ 

[1] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

关键词: Baire's Theorem;    Generic property;    Differentiation and integration operators;    Taylor expansion;    Partial sums;    Universal Taylor series;   

DOI  :  10.1016/j.jmaa.2017.08.025

来源: Elsevier

【 摘 要 】

In this article we prove a general result which in particular suggests that, on a simply connected domain Omega in C, all the derivatives and anti-derivatives of the generic holomorphic function are unbounded. A similar result holds for the operator (T) over tilde (N) of partial sums of the Taylor expansion with center zeta is an element of Omega at z = 0, seen as functions of the center zeta. We also discuss a universality result of these operators (T) over tilde (N). (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free