Approximation of Besov vectors by Paley-Wiener vectors in Hilbert spaces

TL;DR

This paper develops a generalized approximation theory in Hilbert spaces, extending classical methods to enhance data processing tasks like compression and denoising, with applications in harmonic analysis, machine learning, and computer vision.

Contribution

It introduces a new approximation framework for Besov vectors using Paley-Wiener vectors, broadening the scope of harmonic analysis on manifolds and graphs.

Findings

Enables improved data representation and compression techniques.

Facilitates advanced denoising and visualization methods.

Extends classical approximation theory to new mathematical settings.

Abstract

We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data representation, compression, denoising and visualization. These tasks are of great importance to machine learning, complex data analysis and computer vision.