On multi-dimensional sampling and interpolation
Classical Analysis and ODEs
2013-04-03 v1 Functional Analysis
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.
Cite
@article{arxiv.1304.0648,
title = {On multi-dimensional sampling and interpolation},
author = {Alexander Olevskii and Alexander Ulanovskii},
journal= {arXiv preprint arXiv:1304.0648},
year = {2013}
}