Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

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.