, Volume 3, Issue 4, pp 309-341

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.