Approximations in $L_{p}$-norms and Besov spaces on compact manifolds

TL;DR

This paper characterizes Besov spaces on compact Riemannian manifolds through best approximation by eigenfunctions of elliptic operators, extending classical approximation theory to geometric settings.

Contribution

It introduces a novel approach to describe Besov spaces on manifolds using eigenfunction approximations, generalizing existing Euclidean results.

Findings

Besov spaces characterized via eigenfunction approximation

Extension of approximation theory to Riemannian manifolds

Framework applicable to various elliptic operators

Abstract

The objective of the paper is to describe Besov spaces on general compact Riemannian manifolds in terms of the best approximation by eigenfunctions of elliptic differential operators.