Advances in Gabor Analysis [Hardcover]

Hans G. Feichtinger (Editor), Thomas Strohmer (Editor)

Book Description

ISBN-10: 0817642390 | ISBN-13: 978-0817642396 | Publication Date: December 6, 2002 | Edition: 1

Unified, self-contained volume providing insight into the richness of Gabor analysis and its potential for development in applied mathematics and engineering. Mathematicians and engineers treat a range of topics, and cover theory and applications to areas such as digital and wireless communications. The work demonstrates interactions and connections among areas in which Gabor analysis plays a role: harmonic analysis, operator theory, quantum physics, numerical analysis, signal/image processing. For graduate students, professionals, and researchers in pure and applied mathematics, math physics, and engineering.

Editorial Reviews

Review

"The authors have put their effort into writing articles with the necessary background to make their presentations attractive and including a complete set of references. Good introductions and detailed expositions of ideas are given in all the presentations. These features make this book an invaluable tool for researchers interested in signal analysis. The research community will benefit greatly from this publication." —Mathematical Reviews

"The present book can be considered as a continuation of two previous ones: Gabor Analysis and Algorithms: Theory and Applications, H. G. Feichtinger and T. Strohmer, Eds., Birkhäuser 1998, and the book by K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser 2001. It contains survey chapters, but new results that have not been published previously are also included. The introductory chapter of the book, written by H. G. Feichtinger and T. Strohmer, contains a clear outline of the contents as well as some comments on the future developments in Gabor analysis.

Written by leading experts in the field, the volume appeals, by its interdisciplinary character, to a large audience, both novices and experts, theoretically inclined researchers and practitioners as well. It brilliantly illustrates how application areas and pure and applied mathematics can work together with profit for all." —Revue D'Analyse Numérique et de Théorie de L'Approximation, 2004

"A mathematically sound and self-contained presentation on recent advances in the highly applicable field of Gabor analysis.… This book is a must for all interested in signal analysis, and, of course, in particular in Gabor analysis." —Monatschefte für Mathematik

 

Product Details

• Hardcover: 368 pages
• Publisher: Birkhäuser Boston; 1 edition (December 6, 2002)
• Language: English
• ISBN-10: 0817642390
• ISBN-13: 978-0817642396
• Product Dimensions: 9.3 x 6 x 0.9 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,776,595 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars A gem of a book, February 13, 2003

By 

Peter G. Casazza (Columbia, MO) - See all my reviews

This review is from: Advances in Gabor Analysis (Hardcover)

This book contains a series of chapters which represent
a comprehensive analysis of some of the most important
topics in Gabor analysis as well as important new results
in these areas. The chapter on ``uncertainty principles''
finally brings the full scope of this important topic to
light - far beyond the ``classical uncertainty principle''.
One of the deepest questions in Gabor analysis is the
classification of the g,a,b so that (g,a,b) yields a Gabor
frame. Chapter 3 of this book gives a comprehensive
study of the case where g is the characteristic function
of an interval, showing that even this case is quite complicated
and not completely resolved yet. Operator Algebras are
playing an ever more important role in Gabor frame theory
and Chapter 6 gives one a glimpse into these powerful
techniques - especially in analyzing ``subspace Gabor frames''.
For applications, one needs to invert the frame operator.
These is a whole section in the book on the most up to
date results on inverting the Gabor frame operator.
One can also find other important gems in the book such as an
important introduction to pseudodifferential operators and
applications of Weyl-Heisenberg sets of stochastic encoding.
This is just a portion of the important topics in the book.
The chapters are very well written by leading experts in the
field, which allows one to ``get into'' a topic even with little
previous knowledge. Therefore, it is invaluable for people
who want to enter one of these areas of Gabor analysis for
the first time. Overall, this book is a significant contribution
to Gabor analysis and should sit on the desk of anyone working
in this area.