local linear independence
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2006 ◽  
Vol 44 (6) ◽  
pp. 2389-2407 ◽  
Author(s):  
Jörg Peters ◽  
Xiaobin Wu


Author(s):  
T. N. T. Goodman ◽  
R.-Q. Jia ◽  
D.-X. Zhou

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.



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




1985 ◽  
Vol 82 (3) ◽  
pp. 243-263 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Charles Micchelli


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