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, Volume 95, Issue 1, pp 137–147 | Cite as

Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

  • Holger Boche
Article
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Abstract

The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous functiong 1 εC 0[0,1]2 with support in the rectangle [0,1]×[0,1/2] is indicated in the paper for which the two dimensional Shannon sampling series diverge almost everywhere in the rectangle [0,1]×[1/2,1]. This shows that the localization principle for Shannon sampling series cannot hold in two dimensions and in higher dimensions. The result solves a problem formulated by P.L. Butzer.

Mathematics Subject Classification (1991)

41A05 94A05 

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Holger Boche
    • 1
    • 2
    • 3
  1. 1.Mathematisches Institut Fakultät für Mathematik und InformatikFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbHBerlinGermany
  3. 3.ETH Zürich, Institut für Kommunikationstechnik, ETH-ZentrumZürich

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