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Subdivision schemes inL p spaces

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    Rong-Qing Jia

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  1. Rong-Qing Jia
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Jia, RQ. Subdivision schemes inL p spaces. Adv Comput Math 3, 309–341 (1995). https://doi.org/10.1007/BF03028366

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  • DOI: https://doi.org/10.1007/BF03028366

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