数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (4): 377-383.
张青
Zhang Qing
摘要： 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.