On 2-dimensional mobile sampling

TL;DR

This paper establishes necessary and sufficient conditions for families of planar curves to serve as stable sampling sets for Bernstein and Paley-Wiener spaces in two dimensions, advancing understanding of mobile sampling in these function spaces.

Contribution

It provides new criteria characterizing when families of planar curves enable stable sampling in Bernstein and Paley-Wiener spaces, clarifying the mobile sampling property.

Findings

Conditions for stable sampling are derived for planar curve families.

Results apply to Bernstein spaces over convex sets in 2.

The work clarifies the mobile sampling property for Paley-Wiener spaces.

Abstract

Necessary and sufficient conditions are presented for several families of planar curves to form a set of stable sampling for the Bernstein space $\mathcal{B}_{\Omega}$ over a convex set $\Omega \subset \mathbb{R}^2$. These conditions "essentially" describe the mobile sampling property of these families for the Paley-Wiener spaces $\mathcal{PW}^p_{\Omega},1\leq p<\infty$.