An Introduction to Frames and Riesz Bases

An Introduction to Frames and Riesz Bases Review

The subject of the book is a new tool in math, with a host of exciting applications. Of course, the subject has roots in classical ideas from harmonic analysis. But the book covers an explosive and exciting variety of developments since roughly 1990, and it is presented in the form of a graduate text. The basic idea begins with linear algebra, and progresses to expansions in function spaces, and multiresolutions. It will be useful to anyone who wants to learn from scratch about the underlying principles, the new results, and the applications. It is well written. A student of mine picked it up accidentally from my desk, and couldn't put it down. After awhile, he had completely forgotten what he came to see me about. It could have been some of the applications, such as antenna theory, wavelets, time-frequency analysis, uses in Radar, speech processing...

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The theory for frames and bases has developed rapidly in recent years because of its role as a mathematical tool in signal and image processing. In this self-contained work, frames and Riesz bases are presented from a functional analytic point of view, emphasizing their mathematical properties. This is the first comprehensive book to focus on the general properties and interplay of frames and Riesz bases, and thus fills a gap in the literature.

Key features:

* Basic results presented in an accessible way for both pure and applied mathematicians

* Extensive exercises make the work suitable as a textbook for use in graduate courses

* Full proofs included in introductory chapters; only basic knowledge of functional analysis required

* Explicit constructions of frames with applications and connections to time-frequency analysis, wavelets, and nonharmonic Fourier series

* Selected research topics presented with recommendations for more advanced topics and further reading

* Open problems to stimulate further research

"An Introduction to Frames and Riesz Bases" will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference.

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*** Product Information and Prices Stored: Apr 24, 2010 10:52:29

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