Abstract:
The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous function g 1∈C 0 [0,1]2 with support in the rectangle [0,1] × [0,½] is indicated in the paper for which the two dimensional Shannon sampling series diverge almost everywhere in the rectangle [0,1] × [½,1]. 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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Received: 21 December 1995 / Revised version: 5 October 1996
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Boche, H. Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen . manuscripta math. 95, 137–147 (1998). https://doi.org/10.1007/PL00005847
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DOI: https://doi.org/10.1007/PL00005847