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Multidimensional Irregular Sampling of Band-Limited Functions in Lp-Spaces

  • Hans G. Feichtinger
  • Karlheinz Gröchenig
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 90)

Abstract

It is the purpose of this note to present a qualitative approach to irregular variants of the so-called Sampling theorem for band-limited functions on ℝm. The basic assertion is the following: Given a compact subset Ω ⊆ ℝm there is critical sampling rate δ00(Ω) > 0 such thatany band-limited f ∈ LP(ℝm) with spec f ⊆ Ω can be completely reconstructed from the sampling values (f(xi)i∈I at any δ0-dense discrete family of points X = (xi)i∈I. The reconstruction will be obtained by an iterative procedure yielding a sequence of smooth approximations of f, convergent to f in the LP-sense for 1 ≤ p < ∞.

Keywords

Sampling Theorem Convolution Product Smooth Approximation Compact Neighborhood Voronoi Region 
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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Hans G. Feichtinger
    • 1
  • Karlheinz Gröchenig
    • 2
  1. 1.Institut für MathematikUniversität WienÖsterreich
  2. 2.Department of Mathematics U-9University of ConnecticutUSA

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