Juergen Mueller (University of Trier, Germany)

will speak on

Simultaneous Polynomial Approximation and Universality Properties of Taylor Series

Time: 4:00PM
Date: Tue 26th March 2019
Location: Seminar Room SCN 1.25 [map]

Abstract: Let $H(\Delta)$ denote the space of functions holomorphic in the unit disc $\Delta$ endowed with the topology of locally uniform convergence. It is known that for a residual set of functions in $H(\Delta)$ the partial sums of the Taylor series behave extremely erratic outside $\Delta$. According to classical results, for functions in Banach spaces of holomorphic functions in $\Delta$ as for example the Hardy spaces or the Dirichlet space the situation is quite different. We show that, however, to a certain extend erratic behaviour still occurs. As a basic tool, results on simultaneous approximation by polynomials play a role.

(This talk is part of the Analysis series.)

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