Consistent sampling of Paley-Wiener functions on graphons

TL;DR

This paper develops sampling methods for Paley-Wiener functions on graphons, extending graph sampling techniques to a continuous setting and establishing conditions for consistent sampling as graphons converge.

Contribution

It introduces a generalized sampling framework for Paley-Wiener functions on graphons and provides conditions for sampling consistency with graphon convergence.

Findings

Sampling methods are adapted for graphon setting.

Conditions for sampling consistency are derived.

Framework generalizes graph sampling to continuous graph limits.

Abstract

We study sampling methods for Paley-Wiener functions on graphons, thereby adapting and generalizing methods initially developed for graphs to the graphon setting. We then derive conditions under which such a sampling estimate is consistent with graphon convergence.