$s$-Numbers of Embeddings of Weighted Wiener Algebras

Abstract

In this paper we study the asymptotic behavior of Kolmogorov, approximation, Bernstein and Weyl numbers of embeddings ${\mathcal{A}}_{\mathrm{mix}}^{s,r}({\mathbb{T}}^d)\to L_2({\mathbb{T}}^d)$ and ${\mathcal{A}}_{\mathrm{mix}}^{s,r}({\mathbb{T}}^d)\to \mathcal{A}({\mathbb{T}}^d)$, where ${\mathcal{A}}_{\mathrm{mix}}^{s,r}({\mathbb{T}}^d)$ is a weighted Wiener algebra of mixed smoothness $s$ and $\mathcal{A}({\mathbb{T}}^d)$ is the Wiener algebra itself, both defined on the $d$-dimensional torus ${\mathbb{T}}^d$. Our main interest consists in the calculation of the associated asymptotic constants.

25 pages