## 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.

### Ágrip:

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 $x\in \mathbb R$. I will show what the obstructions are for doing this kind of approximations, and, most importantly, how all this generalizes to several complex variables.