Smoothness of Multiple Refinable Functions and Multiple Wavelets

@article{Jia1999SmoothnessOM,
  title={Smoothness of Multiple Refinable Functions and Multiple Wavelets},
  author={Rong-Qing Jia and Sherman D. Riemenschneider and Ding-Xuan Zhou},
  journal={SIAM J. Matrix Analysis Applications},
  year={1999},
  volume={21},
  pages={1-28}
}
We consider the smoothness of solutions of a system of refinement equations written in the form φ = ∑ α∈Z a(α)φ(2 · − α), where the vector of functions φ = (φ1, . . . , φr) is in (Lp(R)) and a is a finitely supported sequence of r× r matrices called the refinement mask. We use the generalized Lipschitz space Lip∗(ν, Lp(R)), ν > 0, to measure smoothness of a given function. Our method is to relate the optimal smoothness, νp(φ), to the p-norm joint spectral radius of the block matrices Aε, ε = 0… CONTINUE READING
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