Acta mathematica scientia,Series B ›› 1994, Vol. 14 ›› Issue (4): 377-383.
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Zhang Qing
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Abstract: Given a sequence {b(j), j ∈ Z}, let φ be the compactly supported distribution solution to following refinement equation:φ=∑j∈Zb(j)φ(r·-j) we derive necessary and sufficient conditions for orthogonality, stability and linear independence of integer translates of φ. These conditions are mainly based on the location of the zeros of symbol b(z)=∑j∈Zb(j)z'. Such φ can generate a multiresolution analysis.
Zhang Qing. CONDITIONS OF ORTHOGONALITY AND STABILITY ASSOCIATED WITH THE GENERAL REFINEMENT EQUATION[J].Acta mathematica scientia,Series B, 1994, 14(4): 377-383.
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