Subdivision schemes inLp spaces
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- Jia, RQ. Adv Comput Math (1995) 3: 309. doi:10.1007/BF03028366
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Subdivision schemes play an important role in computer graphics and wavelet analysis. In this paper we are mainly concerned with convergence of subdivision schemes inLp spaces (1≤p≤∞). We characterize theLp-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.