Local Linear Independence of Refinable Vectors of Functions
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چکیده
This paper is devoted to a study of local linear independence of refinable vectors of functions. A vector of functions φ = (φ1, . . . , φr) ∈ (C(IR))r is said to be refinable if it satisfies the vector refinement equation φ(x) = ∑ α∈Z s a(α)φ(2x− α), 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. Local Linear Independence of Refinable Vectors of Functions
منابع مشابه
Properties of locally linearly independent refinable function vectors
where j is in KÁo (A) if Áo(¢ ¡ j) 6 ́ 0 on A. The function vector © is said to be globally linearly independent if in the above de ̄nition A = IR. Hence, local linear independence of © implies global linear independence. For re ̄nable functions (r = 1) with dilation parameter 2 local and global linear independence are equivalent. However, for r > 1 this is not longer true. The description of loca...
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تاریخ انتشار 1998