Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces
- Cite this article as:
- Aldroubi, A. & Gröchenig, K. The Journal of Fourier Analysis and Applications (2000) 6: 93. doi:10.1007/BF02510120
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Under the appropriate definition of sampling density Dϕ, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if Dϕ≥1. This result is similar to Landau's result for the Paley-Wiener space B1/2. If the shift invariant space consists of polynomial splines, then we show that Dϕ<1 is sufficient for the stable reconstruction of a function f from its samples, a result similar to Beurling's special case B1/2.