Description
Book SynopsisTrade ReviewThe presentation of the material is very clear and illustrated by a number of enlightening figures. Many motivating remarks and discussions are provided. A number of proofs in the more elementary chapters are omitted, but precise pointers to the literature are given. Also numerous exercises are posed as well as some more involved 'projects' which motivate the reader to get active herself." - R. Steinbauer,
Monatshefte für Mathematik"This is a gentle introduction to Fourier analysis and wavelet theory that requires little background but still manages to explain some of the applications of Fourier and wavelet methods and touch on several current research topics. ... The authors have taken care to be accessible to undergraduate mathematicians. ... Compared to standard texts, this book is characterised by more personal and historical information, including footnotes. ... It comes with many projects for interested students, and lists a number of open-ended problems that suggest further developments and should engage interested students. ... In summary, this is a well-written and lively introduction to harmonic analysis that is accessible and stimulating for undergraduates and instructive and amusing for the more sophisticated reader. It could also be argued that the material herein should be part of the knowledge of most undergraduates in mathematics, given that the modern world relies more and more on data compression. It is therefore timely as well. It has certainly earned my enthusiastic recommendation." - Michael Cowling,
Gazette of the Australian Mathematical Society"A wonderful introduction to harmonic analysis and applications. The book is intended for advanced undergraduate and beginning graduate students and it is right on target. Pereyra and Ward present in a captivating style a substantial amount of classical Fourier analysis as well as techniques and ideas leading to current research. ... It is a great achievement to be able to present material at this level with only a minimal prerequisite of advanced calculus and linear algebra and a set of Useful Tools included in the appendix. I recommend this excellent book with enthusiasm and I encourage every student majoring in math to take a look." - Florin Catrina,
MAA Reviews"[T]he panorama of harmonic analysis presented in the book includes very recent achievements like the connection of the dyadic shift operator with the Hilbert transform. This gives to an interested reader a good chance to see concrete examples of contemporary research problems in harmonic analysis. I highly recommend this book as a good source for undergraduate and graduate courses as well as for individual studies." - Krzysztof Stempak,
Zentralblatt MATHTable of Contents
- Contents
- List of figures
- List of tables
- IAS/Park City Mathematics Institute
- Preface
- Fourier series: Some motivation
- Interlude: Analysis concepts
- Pointwise convergence of Fourier series
- Summability methods
- Mean-square convergence of Fourier series
- A tour of discrete Fourier and Haar analysis
- The Fourier transform in paradise
- Beyond paradise
- From Fourier to wavelets, emphasizing Haar
- Zooming properties of wavelets
- Calculating with wavelets
- The Hilbert transform
- Useful tools
- Alexander’s dragon
- Bibliography
- Name index
- Subject index
