Session III.5 - Information-Based Complexity
Tuesday, June 20, 17:00 ~ 17:30
Approximation and tractability of isotropic Sobolev embeddings with increasing smoothness
Thomas Kühn
University of Leipzig, Germany - This email address is being protected from spambots. You need JavaScript enabled to view it.
Let $H^s(\mathbb{T}^d)$ be the isotropic Sobolev space of smoothness $s \gt 0$ on the $d$-dimensional torus. In the talk the influence of increasing smoothness on the approximation problem for the embeddings $H^{s(d)}(\mathbb{T}^d)\hookrightarrow L_2(\mathbb{T}^d)$, $d\in\mathbb{N}$, is studied. More precisely, I will give necessary and sufficient conditions for strong polynomial, polynomial, quasi-polynomial, weak and uniformly weak tractability in terms of growth conditions on the smoothness parameters $s(d)$ as $d\to\infty$.