Geodesic
On The Convolution of a Box Spline With a Compactly Supported Distribution: Linear Independence for the Integer Translates
Canadian journal of mathematics, Tome 43 (1991) no. 1, pp. 19-33

Voir la notice de l'article provenant de la source Cambridge University Press

The problem of linear independence of the integer translates of μ * B, where μ is a compactly supported distribution and B 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 μ on certain linear manifolds associated with B. The proof of our result makes an essential use of the necessary and sufficient condition derived in [12]. Several applications to specific situations are discussed. Particularly, it is shown that if the support of μ is small enough then linear independence is guaranteed provided that does not vanish at a certain finite set of critical points associated with B. Also, the results here provide a new proof of the linear independence condition for the translates of B itself.
DOI : 10.4153/CJM-1991-002-7
Mots-clés : box splines, exponential box splines, compactly supported functions, integer translates, linear independence, multivariate splines, 41A63, 41A15 
Chui, Charles K.; Ron, Amos. On The Convolution of a Box Spline With a Compactly Supported Distribution: Linear Independence for the Integer Translates. Canadian journal of mathematics, Tome 43 (1991) no. 1, pp. 19-33. doi: 10.4153/CJM-1991-002-7
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