Best $n$-term approximation of diagonal operators and application to function spaces with mixed smoothness

TL;DR

This paper precisely determines the best $n$-term approximation widths of diagonal operators between sequence spaces and applies these results to analyze the approximation of function space embeddings with mixed smoothness.

Contribution

It provides exact values for approximation widths of diagonal operators and applies these findings to function space embeddings with mixed smoothness.

Findings

Exact values of approximation widths for diagonal operators between $\, ext{ell}_p$ and $ ext{ell}_q$ spaces.

Asymptotic constants for approximation widths of function space embeddings.

Application to trigonometric system approximations in function spaces.

Abstract

In this paper we give exact values of the best $n$-term approximation widths of diagonal operators between $\ell_p(\mathbb{N})$ and $\ell_q(\mathbb{N})$ with $0<p,q\leq \infty$. The result will be applied to obtain the asymptotic constants of best $n$-term approximation widths of embeddings of function spaces with mixed smoothness by trigonometric system.