Über gewisse nichtfortsetzbare Potenzreihen. II.
Ueber das Verhalten gewisser Potenzreihen auf dem Convergenzkreise
Ueber die sprungweisen Werthänderungen analytischer Functionen
Universal functions on nonsimply connected domains
We establish certain properties for the class of universal functions in with respect to the center , for certain types of connected non-simply connected domains . In the case where is discrete we prove that this class is -dense in , depends on the center and that the analog of Kahane’s conjecture does not hold.
Universal Taylor series, conformal mappings and boundary behaviour
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Universal Taylor series with maximal cluster sets.
Universally divergent Fourier series via Landau's extremal functions
We prove the existence of functions , the Fourier series of which being universally divergent on countable subsets of . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on .
Теорема Харди-Литлвуда в областях с квазиконформной границей и ее приложения к гармоническим функциям
Теоремы типа А.Островского и инвариантные подпространства аналитических функций