First Course on Wavelets FROM THE PUBLISHER
This unique book is an excellent introduction to the basic properties of wavelets. The fundamental construction of these functions by means of "multiresolution analyses" is presented; in particular, this method is used for introducing the spline wavelets and the compactly supported wavelets. An important feature of this book, however, is the use of the Fourier transform for studying wavelets on the real line. A simple characterization of all wavelets is presented which is most useful for the construction of new families of wavelets. This technique can also be used for obtaining characterizations of low pass filters and scaling functions. Another feature is the use of wavelets for representing those function spaces that are most often encountered in analysis: the Lebesgue spaces, Hardy spaces, and more generally, the Besov spaces, the Sobolev, and the Lipschitz spaces. Other topics, some related to applications, are also included: the Fast Fourier Transform, wavelet packets, frames, local cosine and sine bases and their discrete versions are just some examples.
FROM THE CRITICS
Booknews
An introduction to the basic properties of wavelets, for mathematicians, engineers, physicists, and graduate students familiar with the Fourier transform and its basic properties. Illustrates the construction of these algorithms by means of multiresolution analyses, and shows how they can be used in applications to characterize various stypes of function spaces. Contains chapters on sine and cosine bases, band-limited wavelets, representation of functions and function space, frames, and discrete transforms and algorithms. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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