FoCM 2014 conference

Workshop B5 - Information Based Complexity

December 16, 17:30 ~ 18:00 - Room B23

## Optimal Approximation of Sobolev Functions in the $L_2$ and in the Supremum Norm

### Winfried Sickel

### Friedrich-Schiller-University Jena , Germany - winfried.sickel@uni-jena.de

Using tools taken from the theory of operator ideals and $s$-numbers, we develop a general approach to transfer estimates for $L_2$-approximation of Sobolev functions into results for $L_\infty$-approximation under a detailed control of all involved constants. As illustration, we derive some results for isotropic Sobolev spaces $H^s (\mathbb{T}^d)$ and Sobolev spaces of dominating mixed smoothness $H^s _{\text{mix}} (\mathbb{T}^d)$, always equipped with natural norms. Also some comments to related questions for Besov spaces will be given.

Joint work with Fernando Cobos (Universidad Complutense de Madrid, Spain) and Thomas Kuehn (University of Leipzig, Germany).