$s$-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}^{s,r}_{\rm mix}(\mathbb{T}^d) \to L_2(\mathbb{T}^d)$ and $\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to \mathcal{A}(\mathbb{T}^d)$, where $\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d)$ 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.