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Macmillan Higher Education

Classical Fourier Analysis (3rd Edition)

Author(s):
Publisher:

Springer

Pages: 638
Further Actions:

Recommend to library

AVAILABLE FORMATS

Hardcover - 9781493911936

26 November 2014

$89.99

In stock


Paperback - 9781493939169

03 August 2016

$89.99

In stock

Ebook - 9781493911943

17 November 2014

$89.99

In stock

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...

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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.

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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

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.

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

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

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