Benedikt Magnússon (22/09/14)

Benedikt Magnússon, September 17, 2014

Math Colloquium

Speaker: Benedikt Magnússon
Title: Carleman approximations

Location: V-157, VRII
Time: Monday September 22, at 15:00-16:00.

Abstract:

I will introduce Carleman’s remarkable extension of the Weierstrass approximation theorem. In its simplest form it states that if \(f\) and \(\epsilon\) are continuous functions on the real line \(\mathbb R \subset \mathbb C\), and \(\epsilon > 0\) then there exists an entire function \(F\) such that \(\)|f(x)-F(x)| < \epsilon(x)[/latex], for all [latex]x\in \mathbb R[/latex]. I will show what the obstructions are for doing this kind of approximations, and, most importantly, how all this generalizes to several complex variables.