The chapter reviews geometric constructions for averages, subdivision, and multiresolution transforms on metric spaces, Riemannian manifolds, and groups, with emphasis on convergence and smoothness results.
Yu, Smoothness equivalence properties of interpolatory Lie group sub- division schemes, IMA J
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Geometric subdivision and multiscale transforms
The chapter reviews geometric constructions for averages, subdivision, and multiresolution transforms on metric spaces, Riemannian manifolds, and groups, with emphasis on convergence and smoothness results.