Overview
- Historical notes at the end of each chapter
- Numerous exercises for each chapter
- User-friendly exposition with examples illustrating the definitions and ideas
Part of the book series: Graduate Texts in Mathematics (GTM, volume 249)
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About this book
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.
While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. Asa result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...).
From a review of the first edition:
“Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
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Keywords
Table of contents (5 chapters)
Reviews
From a reviews:
“Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
From the reviews of the second edition:
"The author … has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. … Classical Fourier Analysis also comes equipped with a wealth of exercise … and each chapter is capped off by a wonderful ‘Historical Notes’ … . I think it’s nigh-on indispensable for the aspiring Fourier analyst." (Michael Berg, MAA Online, January, 2009)
“Intended for graduate students who wish to study Fourier analysis. … also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. … certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises.” (Andreas Seeger, Mathematical Reviews, Issue 2011 c)
“This book is intended to present the selected topics in depth and to stimulate further study in Fourier analysis. … proofs are provided in great detail and a large amount of exercises of varying difficulty were carefully prepared by the author … . This book is very interesting and useful. It is not only a good textbook, but also an indispensable and valuable reference for researchers … . The readers will certainly benefit a lot from the detailed proofs and the numerous exercises.” (Yang Dachun, Zentralblatt MATH, Vol. 1220, 2011)
Bibliographic Information
Book Title: Classical Fourier Analysis
Authors: Loukas Grafakos
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-09432-8
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2008
Softcover ISBN: 978-1-4419-1855-0Published: 19 November 2010
eBook ISBN: 978-0-387-09432-8Published: 18 September 2008
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XVI, 492
Number of Illustrations: 10 b/w illustrations
Additional Information: Originally published by Prentice Hall
Topics: Analysis, Fourier Analysis, Abstract Harmonic Analysis, Functional Analysis