On 2-dimensional mobile sampling

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

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