Benedikt Magnússon (22/09/14)

Benedikt Magnússon, september 17, 2014

Málstofa í stærðfræði

Fyrirlesari: Benedikt Magnússon
Titill: Carleman approximations

Staðsetning: V-157, VRII
Tími: Mánudagur 22. september, frá 15:00 til 16:00.


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.