Complex Analysis Seminar
Mark Lawrence
Nazarbayev University
The 1-dimensional extension property in complex analysis
Abstract: A classical theorem states that if a function on the unit circle has
vanishing negative Fourier coefficients, then it extends to holomorphic
function on the unit disc. What happens when you are given a family of
curves, and a function which extends holomorphically from each of the
curves? This area of study is called the "1-dimensional extension
problem". Results for planar domains, and for holomorphic extension from
boundaries in C^n will be discussed. One application is the construction
of a completely new class of algebras of real analytic functions.
Various techniques of analytic extension in several variables are used
to prove these results.
Wednesday November 22, 2017 at 3:00 PM in SEO 1227