Full length article: The classical and approximate sampling theorems and their equivalence for entire functions of exponential type

  • Authors:

  • P. L. Butzer;G. Schmeisser;R. L. Stens

  • Affiliations:

  • -;-;-

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2014

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Abstract

It is shown that three versions of the sampling theorem of signal analysis are equivalent in the sense that each can be proved as a corollary of one of the others. The theorems in question are the sampling theorem for functions belonging to the Bernstein space B"@s^2, the sampling theorem for functions in B"@t^~, 0