Stability and Linear Independence Associated with Scaling Vectors

  title={Stability and Linear Independence Associated with Scaling Vectors},
  author={Jianzhong Wang},
In this paper, we discuss stability and linear independence of the integer translates of a scaling vector = (1 ; ; r) T , which satisses a matrix reenement equation (x) = n X k=0 P k (2x ? k); where (P k) is a nite matrix sequence. We call P (z) = 1 2 P P k z k the symbol of. Stable scaling vectors often serve as generators of multiresolution analyses (MRA) and therefore play an important role in the study of multiwavelets. Most useful MRA generators are also linearly independent. The purpose… CONTINUE READING

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