Smoothness of Multiple Refinable Functions and Multiple Wavelets

  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},
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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Regularity of refinable function vectors

  • A. Cohen, I. Daubechies, G. Plonka
  • J. Fourier Anal. Appl., 3
  • 1997
Highly Influential
13 Excerpts

Refinable function vectors

  • Z. Shen
  • SIAM J. Math. Anal., 29
  • 1998
Highly Influential
8 Excerpts

Existence of multiple refinable distributions

  • D. X. Zhou
  • Michigan Math. J., 44
  • 1997
Highly Influential
7 Excerpts

A study of orthonormal multi-wavelets

  • C. K. Chui, J. A. Lian
  • J. Appl. Numer. Math., 20
  • 1996
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11 Excerpts

Stability of refinable functions

  • D.-X. Zhou
  • multiresolution analysis, and Haar bases, SIAM J…
  • 1996
Highly Influential
6 Excerpts

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