The Functional and Harmonic Analysis of Wavelets and Frames: Ams Special Session on the Functional and Harmonic Analysis of Wavelets, January 13-14, 1999, San Antonio, Texas (Contemporary Mathematics) [Paperback]

Texas) AMS Special Session on the Functional and Harmonic Analysis of Wavelets (1999 : San Antonio (Author), Lawrence W. Baggett (Author)

Book Description

Publication Date: December 1999 | ISBN-10: 0821819577 | ISBN-13: 978-0821819579

Over the past decade, wavelets and frames have emerged as increasingly powerful tools of analysis on $n$-dimension Euclidean space. Both wavelets and frames were studied initially by using classical Fourier analysis. However, in recent years more abstract tools have been introduced, for example, from operator theory, abstract harmonic analysis, von Neumann algebras, etc.

The editors of this volume organized a Special Session on the functional and harmonic analysis of wavelets at the San Antonio (TX) Joint Mathematics Meetings. The goal of the session was to focus research attention on these newly-introduced tools and to share the organizers' view that this modern application holds the promise of providing some deeper understanding and fascinating new structures in pure functional analysis. This volume presents the fruitful results of the lively discussions that took place at the conference.

Product Details

• Paperback: 306 pages
• Publisher: Amer Mathematical Society (December 1999)
• Language: English
• ISBN-10: 0821819577
• ISBN-13: 978-0821819579
• Product Dimensions: 9.8 x 6.9 x 0.7 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #8,035,105 in Books (See Top 100 in Books)

Customer Reviews

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1 of 1 people found the following review helpful:

5.0 out of 5 stars wavelets and their cousins, February 4, 2008

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
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This review is from: The Functional and Harmonic Analysis of Wavelets and Frames: Ams Special Session on the Functional and Harmonic Analysis of Wavelets, January 13-14, 1999, San Antonio, Texas (Contemporary Mathematics) (Paperback)

In recent years a number of specializations in mathematics (analysis, geometry and number theory) have come together: Starting with wavelets and their close cousins, we have witnessed ideas from one field connecting and being used in surprising ways in another, and making contacts to such applied areas as Radon transforms, frames, and fractals; and to applications outside of mathematics as well: engineering, physics, and medical imaging. This works in reverse as well, including even applications of ideas from signal processing to mathematics proper!
The book contains several instances of this: For example in the form of wavelet sets, i.e., special affine tilings (wavelet sets and their geometries).
A common core of this multifaceted enterprise involves harmonic analysis (with a computational slant) and symmetry (as understood in the language of representation theory.)
This book is presents a cross section of all of this material in a form that is understandable and attractive to a wider readership, including graduate students in mathematics and its neighboring fields.
Wavelets and related basis constructions, such as frames from engineering, are three decades old (not counting Haar's wavelet.) Their theory and applications are presented here from different angles: harmonic analysis, operator theory, geometry, computations, special tilings, and algorithms. The use of wavelets is compared with other transform tools, Fourier, Radon, Gabor, multiscale and more.
Review by Palle Jorgensen, February 2008.