$s$-Numbers of Embeddings of Weighted Wiener Algebras

TL;DR

This paper investigates the asymptotic behavior of various s-numbers for embeddings of weighted Wiener algebras of mixed smoothness into L2 spaces and Wiener algebras, focusing on asymptotic constants.

Contribution

It provides new asymptotic estimates and constants for the s-numbers of embeddings between weighted Wiener algebras and other function spaces.

Findings

Asymptotic behavior of Kolmogorov, approximation, Bernstein, and Weyl numbers analyzed.

Explicit asymptotic constants calculated for the embeddings.

Results enhance understanding of the approximation properties 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.