On multi-dimensional sampling and interpolation

Alexander Olevskii*, Alexander Ulanovskii

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)149-170
Number of pages22
JournalAnalysis and Mathematical Physics
Issue number2
StatePublished - 25 Jun 2012


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