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On multi-dimensional sampling and interpolation

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Abstract

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 n > 1. While the critical value for sampling sets remains constant, the one for interpolation grows linearly with the dimension.

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Authors and Affiliations

  1. School of Mathematics, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Alexander Olevskii

  2. Stavanger University, 4036, Stavanger, Norway

    Alexander Ulanovskii

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  1. Alexander Olevskii
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  2. Alexander Ulanovskii
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Correspondence to Alexander Olevskii.

Additional information

A. Olevskii is supported in part by the Israel Science Foundation and A. Ulanovskii is supported by an ESF-HCAA grant.

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Olevskii, A., Ulanovskii, A. On multi-dimensional sampling and interpolation. Anal.Math.Phys. 2, 149–170 (2012). https://doi.org/10.1007/s13324-012-0027-4

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  • DOI: https://doi.org/10.1007/s13324-012-0027-4

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