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Robustness of sampling and reconstruction and Beurling–Landau-type theorems for shift-invariant spaces. (English) Zbl 1086.42017

Summary: Beurling-Landau-type results are known for a rather small class of functions limited to the Paley-Wiener space and certain spline spaces. Here, we show that the sampling and reconstruction problem in shift-invariant spaces is robust with respect to two classes of probing measures as well as to the underlying shift-invariant space. As an application we enlarge the class of functions for which Beurling-Landau-type results hold.

MSC:

42C15 General harmonic expansions, frames
41A15 Spline approximation
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
94A20 Sampling theory in information and communication theory
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