Multiresolution analysis on compact Riemannian manifolds

Abstract: In the chapter "Multiresolution Analysis on Compact Riemannian Manifolds" Isaac Pesenson describes multiscale analysis, sampling, interpolation and approximation of functions defined on manifolds. His main achievements are: construction on manifolds of bandlimited and space-localized frames which have Parseval property and construction of variational splines on manifolds. Such frames and splines enable multiscale analysis on arbitrary compact manifolds, and they already found a number of important applications (statistics, CMB, crystallography) related to such manifolds as two-dimensional sphere and group of its rotations.