1996 ◽  
Vol 87 (3) ◽  
pp. 291-327 ◽  
Author(s):  
A. Atzmon ◽  
A. Olevski

1993 ◽  
Vol 36 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Rong-Qing Jia ◽  
Charles A. Micchelli

We investigate linear independence of integer translates of a finite number of compactly supported functions in two cases. In the first case there are no restrictions on the coefficients that may occur in dependence relations. In the second case the coefficient sequences are restricted to be in some lp space (1 ≦ p ≦ ∞) and we are interested in bounding their lp-norms in terms of the Lp-norm of the linear combination of integer translates of the basis functions which uses these coefficients. In both cases we give necessary and sufficient conditions for linear independence of integer translates of the basis functions. Our characterization is based on a study of certain systems of linear partial difference and differential equations, which are of independent interest.


1991 ◽  
Vol 43 (1) ◽  
pp. 19-33 ◽  
Author(s):  
Charles K. Chui ◽  
Amos Ron

AbstractThe 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.


2014 ◽  
Vol 266 (4) ◽  
pp. 2281-2293 ◽  
Author(s):  
Morten Nielsen ◽  
Hrvoje Šikić

1992 ◽  
Vol 78 (1) ◽  
pp. 95-130 ◽  
Author(s):  
N. Dyn ◽  
I. R. H. Jackson ◽  
D. Levin ◽  
A. Ron

2019 ◽  
Vol 106 (1-2) ◽  
pp. 71-80
Author(s):  
E. A. Kiselev ◽  
L. A. Minin ◽  
I. Ya. Novikov

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