A Necessary And Sufficient Condition For The Linear Independence Of The Integer Translates Of A Compactly Supported Distribution (1987)
| Venue: | Constr. Approx |
| Citations: | 35 - 6 self |
BibTeX
@ARTICLE{Ron87anecessary,
author = {Amos Ron and Beverly Sackler},
title = {A Necessary And Sufficient Condition For The Linear Independence Of The Integer Translates Of A Compactly Supported Distribution},
journal = {Constr. Approx},
year = {1987},
volume = {5},
pages = {297--308}
}
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Abstract
Given a multivariate compactly supported distribution OE, we derive here a necessary and sufficient condition for the global linear independence of its integer translates. This condition is based on the location of the zeros of b OE = The Fourier-Laplace transform of OE. The utility of the condition is demonstrated by several examples and applications, showing in particular, that previous results on box splines and exponential box splines can be derived from this condition by a simple combinatorial argument. July, 1987 1980 Mathematics Subject Classification (1985): Primary 41A63, 41A15. Key Words: Box Splines, Exponential Box Splines, Polynomial Box Splines, Integer Translates, Compactly Supported Function, Compactly Supported Distribution, Spectral Analysis, Global Linear Independence, Fourier Transform. 1. Introduction and Statement of Main Results Let E 0 (IR s ) be the space of all s-dimensional complex valued distributions of compact support. For each OE 2 E 0 (IR s ) ...
Citations
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