On the Convolution of a Box Spline with a Compactly Supported Distribution: The Exponential-Polynomials in the Linear Span
Amos Ron and Charles K Chui
The problem of linear independence of the integer translates of where is a compactly supported distribution and is an exponential box spline, is considered in this paper. The main result relates the linear independence issue with the distribution of the zeros of the Fourier-Laplace transform of on certain linear manifolds associated with . The proof of our result makes an essential use of the necessary and sufficient condition derived in . Several applications to specific situations are discussed. Particularly, it is shown that if the support of is small enough then linear independence is guaranteed provided that does not vanish at a certain finite set of critical points associated with . Also, the results here provoke a new proof of the linear independence condition for the translates of itself.
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