Loukas Grafakos: Classical Fourier Analysis

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Cover: 9781441918550 | Classical Fourier Analysis | Loukas Grafakos | Taschenbuch | Paperback

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Sprache: Englisch

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Beschreibung

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

Zusammenfassung

Historical notes at the end of each chapter

Numerous exercises for each chapter

User-friendly exposition with examples illustrating the definitions and ideas

Inhaltsverzeichnis

L Spaces and Interpolation.- Maximal Functions Fourier Transform and Distributions.- Fourier Analysis on the Torus.- Singular Integrals of Convolution Type.- Littlewood#x2013;Paley Theory and Multipliers.

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	508
Reihe:	Graduate Texts in Mathematics
ISBN-13:	9781441918550
ISBN-10:	1441918558
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Grafakos, Loukas
Auflage:	Softcover reprint of hardcover 2nd ed. 2008
Hersteller:	Springer US Springer New York Graduate Texts in Mathematics
Maße:	235 x 155 x 28 mm
Von/Mit:	Loukas Grafakos
Erscheinungsdatum:	19.11.2010
Gewicht:	0,762 kg

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