Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces

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Abstract

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 B 1/2 . 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 B 1/2 .

Communicated by John J. Benedetto