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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…mehr

Produktbeschreibung
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

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

  • Produktdetails
  • Verlag: Springer-Verlag GmbH
  • Erscheinungstermin: 18.09.2008
  • Englisch
  • ISBN-13: 9780387094328
  • Artikelnr.: 37288141
Autorenporträt
Loukas Grafakos is a Professor of Mathematics at the University of Missouri at Columbia.
Inhaltsangabe
Preface.- Lp Spaces and Interpolation.- Maximal Functions, Fourier Transform, and Distributions.- Fourier Analysis on the Torus.- Singular Integrals of Convolution Type.- Littlewood-Paley Theory and Multipliers.- Gamma and Beta Functions.- Bessel Functions.- Rademacher Functions.- Spherical Coordinates.- Some Trigonometric Identities and Inequalities.- Summation by Parts.- Basic Functional Analysis.- The Minimax Lemma.- The Schur Lemma.- The Whitney Decomposition of Open Sets in Rn.- Smoothness and Vanishing Moments.- Glossary.- References.- Index.
Rezensionen
"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)
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