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Classical Fourier Analysis (Graduate Texts in Mathematics, nr. 249)

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en Limba Engleză Paperback – 23 Aug 2016
The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book contains the classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood-Paley theory. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables. This book is intended to present the selected topics in depth and stimulate further study.
This third edition includes a new chapter entitled "Topics on Fourier series," which includes sections on Gibbs phenomenon, summability methods and Jackson's theorem, Tauberian theorems, spherical Fourier inversion, and Fourier transforms on the line. The new chapter ties really well with the material in the existing chapter 3 "Fourier Analysis on the Torus" and will prepare the students for (the existing) chapter 4.
In addition to a new chapter, the third edition contains 1000 different corrections and improvements in the existing text, more examples and applications, new and more relevant hints for the existing exercises, about 20-30 new exercises in the existing chapters, and improved references.
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Specificații

ISBN-13: 9781493939169
ISBN-10: 1493939165
Pagini: 656
Dimensiuni: 155 x 235 x 34 mm
Greutate: 9.77 kg
Ediția: Softcover reprint of the original 3rd ed. 2014
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării: New York, NY, United States

Cuprins

Preface.- 1. Lp Spaces and Interpolation.- 2. Maximal Functions, Fourier Transform, and Distributions.- 3. Fourier Series.- 4. Topics on Fourier Series.- 5. Singular Integrals of Convolution Type.- 6. Littlewood–Paley Theory and Multipliers.- 7. Weighted Inequalities.- A. Gamma and Beta Functions.- B. Bessel Functions.- C. Rademacher Functions.- D. Spherical Coordinates.- E. Some Trigonometric Identities and Inequalities.- F. Summation by Parts.- G. Basic Functional Analysis.- H. The Minimax Lemma.- I. Taylor's and Mean Value Theorem in Several Variables.- J. The Whitney Decomposition of Open Sets in Rn.- Glossary.- References.- Index.

Recenzii

“The most up-to-date account of the most important developments in the area. … It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well” (Atanas G. Stefanov, Mathematical Reviews, August, 2015)

Notă biografică

Loukas Grafakos is a Professor of Mathematics at the University of Missouri at Columbia.

Textul de pe ultima copertă

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study.
This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition.  Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.
Reviews from the Second Edition:
“The books cover a large amount of mathematics. They are 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 Seager, Mathematical Reviews
“This book is very interesting and useful. It is not only a good textbook, but also an
indispensable and valuable reference for researchers who are working on analysis and partial differential equations. The readers will certainly benefit a lot from the detailed proofs and the numerous exercises.” —Yang Dachun, zbMATH

Caracteristici

New edition extensively revised and updated, including 1000 different corrections and improvements in the existing text
Includes a new chapter, "Topics on Fourier series", including sections on Gibbs phenomenon, summability methods and Jackson's theorem, Tauberian theorems, spherical Fourier inversion, and Fourier transforms on the line
Provides motivation for the reader with more examples and applications, new and more relevant hints for the existing exercises, and about 20-30 new exercises in the existing chapters