4- https://doi.org/10.4153/cjm-1991-002-7
On The Convolution of a Box Spline With a Compactly Supported Distribution: Linear Independence for the Integer Translates
- Feb 1, 1991
- Canadian Journal of Mathematics
- Charles K Chui +1 more
Abstract 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.
- # Exponential Box Spline
- # Linear Independence
- # Integer Translates
- # Box Spline
- # Finite Set Of Points
- # Exponential Spline
- # Set Of Points
- # Set Of Critical Points
- # Linear Independence Condition
- # Exponential Box
