Sampling and Uniqueness Sets in Graphon Signal Processing

ArXi:2401.06279v3 Announce Type: replace In this work, we study the properties of sampling sets on families of large graphs by leveraging the theory of graphons and graph limits. To this end, we extend to graphon signals the notion of removable and uniqueness sets, which was developed originally for the analysis of signals on graphs. We state the formal definition of a $\Lambda-$removable set and conditions under which a bandlimited graphon signal can be represented in a unique way when its samples are obtained from the complement of a given $\Lambda-$removable set in the graphon.