Divergenzverhalten mehrdimensionaler Shannonscher Abtastreihen

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,?] is indicated in the paper for which the two dimensional Shannon sampling series diverge almost everywhere in the rectangle 0,1] × ?,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. Received: 21 December 1995 / Revised version: 5 October 1996