“…Precise decay conditions on Φ amount to diverse qualities of the set of molecules, such as number of derivatives, order of decay, and vanishing moments [51,54,61]. In light of (1.10), the molecule condition pertains to the locality of the sampling expansion (1.9), explaining its fundamental role in approximation theory: not only do the samples {W ψ f (λ) : λ ∈ Λ} characterize W ψ f , but the value W ψ f (b, a) can be approximated, up to a well-controlled error, by a finite subset of samples {W ψ f (λ) : λ −1 (b, a) ∈ U }, with U ⊂ G compact.…”