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  • Mathematics Subject Classification (1991): 41A05, 94A05  (1)
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  • Mathematics Subject Classification (1991): 41A05, 94A05  (1)
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    Electronic Resource
    Electronic Resource
    Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen (1998)
    Springer
    Manuscripta mathematica 95 (1998), S. 137-147 
    Details
    ISSN: 1432-1785
    Keywords: Mathematics Subject Classification (1991): 41A05, 94A05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00005847
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