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On multi-dimensional sampling and interpolation

On multi-dimensional sampling and interpolation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

On multi-dimensional sampling and interpolation

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Mathematical Methods in Physics; Analysis
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-012-0027-4
Publisher site
See Article on Publisher Site

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.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Mar 10, 2012

References