On linear independence of integer translates of a finite number of functions (1992)
| Venue: | Proc. Edinburgh Math. Soc |
| Citations: | 69 - 32 self |
BibTeX
@INPROCEEDINGS{Jia92onlinear,
author = {Rong-qing Jia and Charles A. Micchelli},
title = {On linear independence of integer translates of a finite number of functions},
booktitle = {Proc. Edinburgh Math. Soc},
year = {1992},
pages = {69--85}
}
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Abstract
We investigate linear independence of integer translates of a finite number of com-pactly supported functions in two cases. In the first case there are no restrictions on the coefficients that may occur in dependence relations. In the second case the coefficient sequences are restricted to be in some ℓ p space (1 ≤ p ≤ ∞) and we are interested in bounding their ℓ p-norms in terms of the L p-norm of the linear combination of integer translates of the basis functions which uses these coefficients. In both cases we give nec-essary and sufficient conditions for linear independence of integer translates of the basis functions. Our characterization is based on a study of certain systems of linear partial difference and differential equations, which are of independent interest.
