An Introduction to Wavelet Analysis

  • Ole ChristensenEmail author
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In Section 4.7 we introduced orthonormal bases in general Hilbert spaces. The purpose of the current chapter is to present a general way of constructing orthonormal bases with a particular structure in the Hilbert space L 2 (\(\mathbb R\)). In contrast to the other topics treated in the book, wavelet analysis is a quite new topic: although the first constructions appeared about 100 years ago, the systematic analysis began around 1982. In 1987, the key concept of a multiresolution analysis was introduced, and shortly hereafter Daubechies used it to construct a special class of orthonormal bases with attractive properties, e.g., in the context of data compression.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

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