Operators commuting with integration in spaces of functions analytic in simply connected domains

1981 ◽  
Vol 29 (3) ◽  
pp. 209-214
Author(s):  
Yu. A. Kiryutenko
Keyword(s):  
Simply Connected ◽  
Simply Connected Domains

scholarly journals Universal Taylor series for non-simply connected domains

2010 ◽  
Vol 348 (9-10) ◽  
pp. 521-524 ◽  
Author(s):  
Stephen J. Gardiner ◽  
Nikolaos Tsirivas
Keyword(s):  
Taylor Series ◽  
Universal Taylor Series ◽  
Simply Connected ◽  
Simply Connected Domains

Hülder Conditions and the Topology of Simply Connected Domains*

1983 ◽  
Vol 26 (2) ◽  
pp. 189-191
Author(s):  
Dov Aharonov
Keyword(s):  
General Result ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Simply Connected ◽  
Simply Connected Domains

AbstractLet ƒ be regular univalent and normalized in the unit disc U (i.e. ƒ ∊ S) and continuous on U ∈ T, where T denotes the boundary of U.Recently Essén proved [5] a conjecture of Piranian [7] stating that if the derivative of ƒ ∊ S is bounded in U and ƒ(z1) = ƒ(z2) = … = ƒ(zn) for Zj ∊ T, 1 ≤ j ≤ n, then n ≤ 2. In fact, Essén proved a more general result, using a deep result on harmonic functions. The aim of the following article is to replace Essén's proof by a completely different proof which is based only on Goluzin's inequalities and is much more elementary.

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