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> Volume 5, Issue 8
Book: A first course on wavelets

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Guido Weiss (guido@sulu.wustl.edu) Guest

Posted: Mon Sep 09, 1996 5:51 pm Subject: Book: A first course on wavelets




#1 Book: A first course on wavelets
A First Course on Wavelets
Eugenio Hernandez and Guido Weiss
A Volume in the Studies in Advanced Mathematics Series
Series edited by Steven G Krantz
CONTENT:
Wavelet theory had its origin in quantum field theory, signal
analysis, and function space theory. In these areas waveletlike
algorithms replace the classical Fourier typeexpansion of a function.
This unique new book is an excellent introduction to the basic
properties of wavelets, from background math to powerful applications.
The authors provide elementary methods for constructing wavelets, and
illustrate several new classes of wavelets.
The text begins with a description of local sine and cosine bases that
have been shown to be very effective in applications. Very little
mathematical background is needed to follow this material. A complete
treatment of bandlimited wavelets follows. These are characterized
by some elementary equations, allowing the authors to introduce many
new wavelets. Next, the idea of multiresolution analysis (MRA) is
developed, and the authors includ simplified presentations of previous
studies, particularly for compactly supported wavelets.
The authors also present the basic philosophy that all orthonormal
wavelets are completely characterized by two simple equations, and
that most properties and constructions of wavelets can be developed
using these two equations. Material related to applications is
provided, and constructions of splines wavelets are presented.
Mathematics, engineers, physicists, and anyone with a mathematical
background will find this to be an important text for furthering their
studies on wavelets.
SOME OF THE TOPICS TREATED INCLUDE:
 Several bases generatede by a single function via translations and
dilations
 Multiresolution analysis, compactly supported wavelets, and spline
wavelets
 Bandlimited wavelets
 Unconditionality of wavelet bases
 Characterizations of many of the principal objects in the theory of
wavelets, such as lowpass filters and scaling functions
FEATURES:
 Presents several classes of new wavelets
 Subjects that are needed for applications are treated very directly
 Includes many graphic displays of constructed wavelets
 Contains applications to harmonic analysis and other branches of
analysis
ISBN: 0849382742, 512 pp, $64.95
CRC Press, Inc: 18002727737
http://www.crcpress.com/
orders@crcpress.com 





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