Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

Holger Boche

doi:10.1007/PL00005847

Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

Holger Boche

Friedrich Schiller University Jena
Heinrich Hertz Institute
ETH Zurich

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	German
Pages (from-to)	137-147
Number of pages	11
Journal	Manuscripta Mathematica
Volume	95
Issue number	2
DOIs	https://doi.org/10.1007/PL00005847
State	Published - Feb 1998
Externally published	Yes

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10.1007/PL00005847

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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.",

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AB - 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.

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Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

Abstract

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