Pyramids and operators
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In Chapters 4 and 7, we stressed that the crucial feature of Localization is shared by a number of basis constructions, most notably by those of wavelets and of certain classes of fractals. This includes basis constructions in Hilbert spaces built recursively on fractals and on state spaces in dynamics. The recursive approach to the more general basis constructions is a special case of a refined tool from probability which is based on martingales. (It should be contrasted to classical Fourier expansions, which are notoriously poorly localized.)
KeywordsHilbert Space Wavelet Packet Partial Isometry Tensor Factorization Representation Of02
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