Ron, A. Constr. Approx (1989) 5: 297. doi:10.1007/BF01889611
Given a multivariate compactly supported distributionϕ, 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\(\hat \varphi\)=the Fourier-Laplace transform ofϕ. 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.
Key words and phrases
Box splines Exponential box splines Polynomial box splines Integer translates Compactly supported function Compactly supported distribution Spectral analysis Global linear independence Fourier transform