On Linear Dependence Relations for Integer Translates of Compactly Supported Distributions
- 1 January 1991
- journal article
- research article
- Published by Wiley in Mathematische Nachrichten
- Vol. 151 (1) , 303-310
- https://doi.org/10.1002/mana.19911510119
Abstract
A necessary and sufficient condition for the dimension of the space of dependence relations for (multi‐) integer translates of an arbitrary compactly supported distribution in terms of zeros of its Fourier transform is given. We apply this result to obtain necessary and sufficient conditions on an integer matrix X so that the space of dependence relations for the corresponding cube spline C(·|X) is finite dimensional. We are able to describe the explicit form of all dependence relations.Keywords
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