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Optimal approximation of multivariate periodic Sobolev functions in the sup-norm by Cobos, Fernando; Kühn, Thomas; Sickel, Winfried is a scholarly article available to read on EtoBox.

What is Optimal approximation of multivariate periodic Sobolev functions in the sup-norm about?

Using tools 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 estimates for $L_\infty$-approximation, with precise control of all involved constants. As an illustration, we derive some results for periodic isotropic Sobolev spaces $H^s ({\mathbb T}^d)$ and Sobolev spaces of dominating mixed smoothness $H^s_{\rm mix} ({\mathbb T}^d)$, always equipped with natural norms. Some results for isotropic as well as dominating mixed Besov spaces are also obtained.

Author

Cobos, Fernando; Kühn, Thomas; Sickel, Winfried

Published

2015

Language

EN