Local linear independence of the translates of a box spline

1985 ◽  
Vol 1 (1) ◽  
pp. 175-182 ◽  
Author(s):  
Rong-Qing Jia
Keyword(s):  
Linear Independence ◽  
Local Linear ◽  
Box Spline ◽  
Local Linear Independence

scholarly journals On the local linear independence of translates of a box spline

1985 ◽  
Vol 82 (3) ◽  
pp. 243-263 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Charles Micchelli
Keyword(s):  
Linear Independence ◽  
Local Linear ◽  
Box Spline ◽  
Local Linear Independence

Least supported bases and local linear independence

1994 ◽  
Vol 67 (3) ◽  
pp. 289-301 ◽  
Author(s):  
J.M. Carnicer ◽  
J.M. Pe\~na
Keyword(s):  
Linear Independence ◽  
Local Linear ◽  
Local Linear Independence

Local linear independence of refinable vectors of functions

2000 ◽  
Vol 130 (4) ◽  
pp. 813-826 ◽  
Author(s):  
T. N. T. Goodman ◽  
R.-Q. Jia ◽  
D.-X. Zhou
Keyword(s):  
General Theory ◽  
Linear Independence ◽  
Nonlinear Approximation ◽  
Complete Characterization ◽  
Bounded Domains ◽  
Refinement Equation ◽  
Refinement Mask ◽  
Local Linear ◽  
Image Position ◽  
Local Linear Independence

This paper is devoted to a study of local linear independence of refinable vectors of functions. A vector of functions is said to be refinable if it satisfies the vector refinement equation where a is a finitely supported sequence of r × r matrices called the refinement mask. A complete characterization for the local linear independence of the shifts of ϕ1,…,ϕr is given strictly in terms of the mask. Several examples are provided to illustrate the general theory. This investigation is important for construction of wavelets on bounded domains and nonlinear approximation by wavelets.

scholarly journals On The Convolution of a Box Spline With a Compactly Supported Distribution: Linear Independence for the Integer Translates

1991 ◽  
Vol 43 (1) ◽  
pp. 19-33 ◽  
Author(s):  
Charles K. Chui ◽  
Amos Ron
Keyword(s):  
Laplace Transform ◽  
Critical Points ◽  
Linear Independence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compactly Supported ◽  
Integer Translates ◽  
Box Spline ◽  
Finite Set ◽  
Necessary And Sufficient

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.

A Local Linear Wavelet Neural Network Based on a Bayesian Design Method

2009 ◽  
Vol 129 (7) ◽  
pp. 1356-1362
Author(s):  
Kunikazu Kobayashi ◽  
Masanao Obayashi ◽  
Takashi Kuremoto
Keyword(s):  
Neural Network ◽  
Design Method ◽  
Wavelet Neural Network ◽  
Bayesian Design ◽  
Local Linear
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