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Nonlinear multi-scale transforms: \(L_{p}\) theory. (English) Zbl 1319.65014

Summary: We treat the \(L_{p}\) theory (\(1\leq p<\infty \)) for univariate nonlinear subdivision schemes and multi-scale transforms based on the concept of offset invariance and nonlinear derived subdivision operators. The paper covers convergence, smoothness, and stability issues, and complements a recent survey, where results for \(L_{p}\) have been included without proof.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
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