S. Gardiner

will speak on

A strong form of Plessner's theorem I

Time: 4:20PM
Date: Tue 11th February 2020
Location: Seminar Room SCN 1.25 [map]

Abstract: Let f be a holomorphic, or even meromorphic, function on the
unit disc. Plessner's theorem then says that, for almost every boundary point ζ, either (i) f has a finite nontangential limit at ζ, or (ii) the image f(S) of any Stolz angle S at ζ is dense in the complex plane. This
paper shows that statement (ii) can be replaced by a much stronger assertion. This new theorem and its analogue for harmonic functions on halfspaces also strengthen classical results of Spencer, Stein and Carleson.

(This is joint work with Myrto Manolaki.)

(This talk is part of the Analysis series.)

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