Abstract
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.)
Mathematics is an exaperimental science, and definitions do not come first, but later on. —Oliver Heaviside
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© 2006 Springer Science+Business Media, LLC
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(2006). Pyramids and operators. In: Analysis and Probability Wavelets, Signals, Fractals. Graduate Texts in Mathematics, vol 234. Springer, New York, NY. https://doi.org/10.1007/978-0-387-33082-2_8
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DOI: https://doi.org/10.1007/978-0-387-33082-2_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-29519-0
Online ISBN: 978-0-387-33082-2
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