Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

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Abstract

The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous function g1 ∈ C0[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.

Original languageGerman
Pages (from-to)137-147
Number of pages11
JournalManuscripta Mathematica
Volume95
Issue number2
DOIs
StatePublished - Feb 1998
Externally publishedYes

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