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 On multi-dimensional sampling and interpolation


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The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above from below for the distances between interpolation sampling nodes are the same. This is no longer true for n1. While the critical value for sampling sets remains constant, the one for interpolation grows linearly with the dimension.



Author: Alexander Olevskii; Alexander Ulanovskii

Source: https://archive.org/







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