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

Under the appropriate definition of sampling density D-phi, a function f th at belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if D-phi greater than or equal to 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 D-phi < 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.