Wavelets and other phase space localization methods. (English) Zbl 0845.42012

Daubechies, Ingrid

Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. I. Basel: Birkhäuser. 57-74 (1995).

In this very nicely written survey, the authoress discusses the recent development of wavelets, in particular of orthonormal wavelet bases. Following her motive from the introduction, “a wish for beauty and simplicity, and a desire to bring different fields together, can equally well drive developments in ‘applicable’ mathematics”, she explains in a very clear and short way the main ideas and ingredients of wavelets and other related localization methods. As pointed out the main advantage of wavelets is the existence of fast algorithms for reconstruction and decomposition needed in the different applications like subband filtering in electrical engineering or matrix and operator compression. A look on time-frequency localization, wavelet packets and bases of function spaces completes this remarkable survey.
For the entire collection see [Zbl 0829.00014].

Reviewer: J.Prestin (Rostock)

MSC:

42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
42-02	Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces

Keywords:

multiresolution analysis; survey; wavelets; bases; localization; fast algorithms