Article

Journal of Fourier Analysis and Applications

, Volume 6, Issue 1, pp 93-103

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

  • Akram AldroubiAffiliated withDepartment of Mathematics, Vanderbilt University
  • , Karlheinz GröchenigAffiliated withDepartment of Mathematics, Vanderbilt University

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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 .

Math Subject Classifications

42C15 42A65

Keywords and Phrases

irregular sampling spline shift invariant spaces frames Wiener amalgam spaces reproducing Kernel Hilbert spaces