A Necessary and Sufficient Condition for the Linear Independence of the Integer Translates of a Compactly Supported Distribution
نویسنده
چکیده
Given a multivariate compactly supported distribution φ, 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 φ̂ = The Fourier-Laplace transform of φ. 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.
منابع مشابه
Linear Independence of the Integer Translates of Compactly Supported Distributions and Reenable Vectors
Some necessary and suucient conditions in time domain for the global and local linear independence of the integer translates of compactly supported distributions and reenable vectors are established in this paper.
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