Fourier and Wavelet Analysis (Universitext) [Hardcover]

George Bachmann (Author), Lawrence Narici (Author), Edward Beckenstein (Author)

Book Description

Publication Date: December 21, 1999 | ISBN-10: 0387988998 | ISBN-13: 978-0387988993

This comprehensive volume develops all of the standard features of Fourier analysis - Fourier series, Fourier transform, Fourier sine and cosine transforms, and wavelets. The books approach emphasizes the role of the "selector" functions, and is not embedded in the usual engineering context, which makes the material more accessible to a wider audience. While there are several publications on the various individual topics, none combine or even include all of the above.

Editorial Reviews

Review

From the reviews: "This excellent book is intended as an introduction to classical Fourier analysis, Fourier series, Fourier transforms and wavelets, for students in mathematics, physics, and engineering. The text includes many historical notes to place the material in a cultural and mathematical context. The topics are developed slowly for the reader who has neverr seen them before, with a preference for clarity of exposition in stating and proving results." EMS Newsletter, Issue 39, March 2001 "The book under review is intended primarily as an introduction to classical Fourier analysis, Fourier series and Fourier transform. … The discussion is thorough and shows the material at a leisurely pace. There are many exercises that expand on the material, followed by hints or answers. … this book is a reader-friendly, gentle introduction to the theory of Fourier analysis. I recommend this book to graduate or postgraduate mathematics and physics students, engineers, computer scientists and everybody who want to learn Fourier Analysis … ." (Zoltán Németh, Acta Scientiarum Mathematicarum, Vol. 71, 2005) "This book is a self-contained treatise on Fourier analysis and wavelet theory. … is a nice textbook enriched by a lot of historical notes and remarks … . Definitions and results are illustrated by examples. The text, together with the exercises at the end of each section, covers important results. Moreover, most of the exercises are followed by hints on how to solve them, answers or references. Both the style of writing and the contents are quite pleasant and easy to follow … ." (Kathi Karima Selig, Mathematical Reviews, Issue 2001 a) "I enjoyed reading it and learnt quite a lot from it. … The author’s general intention was … to write a book that would present the prerequisites for wavelet theory … . There are also exercises by the way. … and are furnished with ‘hints’ that are usually full solutions. … It is informative, interestingly and clearly written with intelligent comments and pleasing explanations, a delight to read." (Christopher Atkin, The New Zealand Mathematical Society Newsletter, Issue 84, 2002) "Fourier and Wavelet Analysis is primarily an introduction to the theory of Fourier series and Fourier transforms … . There are many sets of exercises that expand on the material in the text, each followed by a corresponding set of hints and/or answers. Accordingly this book is well suited for self-study." (Gerald B. Folland, SIAM Review, Vol. 43 (1), 2000) "The presentation of Fourier Analysis given in this book follows historical development of the subject. … The material is given in the classical style. It is very detailed and self-contained … . Each chapter comes with a collection of exercises." (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 131 (4), 2001) "The text is concerned with the classical theory of Fourier series and transforms … . there are plenty of worked examples and exercises, with hints and solutions. There is also an extensive list of references for readers who wish to investigate further. This is a serious and scholarly work which should be in the library of every mathematics department." (Gerry Leversha, The Mathematical Gazette, Vol. 85 (502), 2001) "This is a good introduction to classical Fourier analysis … . More recent developments such as the discrete and fast Fourier transforms are also covered. … The book includes many historical notes and useful background material from functional analysis." (B. Rubin, Zentralblatt MATH, Vol. 948, 2000) "A specific feature of the book under review is that it combines a simple, clear and intuitive exposition of the results, together with a very rigorous mathematical treatment. … The volume is an excellent text book for graduates and professionals in mathematics, engineering and physical sciences. … . The text includes many historical notes to place the material in a cultural and mathematical context. The main merit of the book is to provide beginners in Fourier analysis with exactly what they are looking for." (B. Kirstein, Zeitschrift für Analysis und ihre Anwendungen, Vol. 19 (3), 2000) "An approachable text for the advanced undergraduate; but perhaps more suitable as a recommended text for early postgraduate study. The text is fluently written with many historical details that puts Fourier’s work into the context of his contemporaries and those who tread his footsteps. Fourier’s series, transforms and wavelet theory are covered in full … ." (ASLIB Book Guide, Vol. 65 (5), 2000)

Product Details

• Hardcover: 533 pages
• Publisher: Springer (December 21, 1999)
• Language: English
• ISBN-10: 0387988998
• ISBN-13: 978-0387988993
• Product Dimensions: 9.5 x 6.1 x 1.2 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,634,959 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

3.0 out of 5 stars Great introduction, but clearly a first edition, December 13, 2001

By 

Matthew Adereth (Pittsburgh, PA USA) - See all my reviews

This review is from: Fourier and Wavelet Analysis (Universitext) (Hardcover)

I'm just finishing a semester-long course which uses this book as an outline and as a source for homework questions. Anyone with basic knowledge of analysis will have no problem picking up this book and learning a great deal about Fourier decomposition and transformations, but there are a few problems with it. The questions at the end of each section don't always make it clear exactly what is to be answered and what is to be assumed. Also, there have been a few questions that neither I, my classmates, nor my professor could solve, which leads me to believe that there are fundamental problems with a few of the questions (I could be wrong though ;) ) Finally, the last chapter seems to use different notation for some things than is used in the rest of the book, so be alert. Overall, the clarity of the material outweighs these flaws and if you have any interest in REALLY understanding Fourier and Wavelet series, get this book.

1 of 3 people found the following review helpful:

4.0 out of 5 stars Very good except for some errors, December 30, 2004

By 

Fernando Sanz Gamiz "Fernando" (Madrid, España Espana) - See all my reviews
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This review is from: Fourier and Wavelet Analysis (Universitext) (Hardcover)

The book is recomendable but it has got several errors. For example, the hint of the exercise 4.7 is not such "hint". Anymore found this or other errors?

Anyway, the exposition is clear and ordered and you will get a great insight on Fourier analyisis.