Bandlimited Lipschitz functions

TL;DR

This paper investigates the properties of bandlimited Lipschitz functions, providing geometric characterizations of their sampling and interpolating sequences, and describing their behavior on critical density sequences through cancellation conditions.

Contribution

It offers a new geometric framework for understanding sampling and interpolation in the space of bandlimited Lipschitz functions, including trace characterizations at critical densities.

Findings

Geometric description of interpolating sequences

Characterization of sampling sequences at critical density

Trace description via cancellation conditions

Abstract

We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of the natural interpolating and sampling sequences for this space. We also find a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.