K. Maronikolakis

will speak on

Universal radial approximation in spaces of analytic functions

Time: 3:00PM
Date: Tue 5th April 2022
Location: Seminar Room SCN 1.25 [map]

Further information

Abstract: Charpentier showed that there exist holomorphic functions $f$ in the unit disk such that, for any proper compact subset $K$ of the unit circle and any continuous function h on K, there exists an increasing sequence $(r_n) \in [0,1)$ converging to 1 such that $|f(r_n \zeta)-h(\zeta)|$ converges to $0$ as $n$ goes to infinity uniformly for $\zeta \in K$. In this talk, I will present analogues of this result for classical Banach spaces of analytic functions. In particular, for the case of the Hardy space $H^p$, we have the following: if we fix a compact subset $K$ of the unit circle with zero arc length measure, then there exist functions in $H^p$ whose radial limits can approximate every continuous function on $K$. I will also make connections with other classes of universal functions.

https://ucd-ie.zoom.us/j/66416459246

(This talk is part of the Analysis series.)

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