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Advances in Computational Mathematics

, Volume 3, Issue 4, pp 309–341 | Cite as

Subdivision schemes inL p spaces

  • Rong-Qing Jia
Article

Abstract

Subdivision schemes play an important role in computer graphics and wavelet analysis. In this paper we are mainly concerned with convergence of subdivision schemes inL p spaces (1≤p≤∞). We characterize theL p -convergence of a subdivision scheme in terms of thep-norm joint spectral radius of two matrices associated with the corresponding mask. We also discuss various properties of the limit function of a subdivision scheme, such as stability, linear independence, and smoothness.

Keywords

Subdivision schemes refinement equations spectral radii stability linear independence smoothness 

AMS subject classification

39B12 41A15 41A25 65D99 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • Rong-Qing Jia
    • 1
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonCanada

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