Classical Fourier analysis
Author(s)
Bibliographic Information
Classical Fourier analysis
（Graduate texts in mathematics, 249）
Springer, c2008
2nd ed
- Other Title
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Classical and modern Fourier analysis
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Note
Previous ed. published under title: Classical and modern Fourier analysis. Pearson/Prentice-Hall, c2004
Includes bibliographical references (p. 473-483) and index
Description and Table of Contents
Description
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. As a 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
Table of Contents
L Spaces and Interpolation.- Maximal Functions Fourier Transform and Distributions.- Fourier Analysis on the Torus.- Singular Integrals of Convolution Type.- Littlewood-Paley Theory and Multipliers.
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