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The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.

Produktbeschreibung
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.
  • Produktdetails
  • Graduate Texts in Mathematics Vol.249
  • Verlag: Springer, Berlin
  • 2nd ed.
  • Seitenzahl: 508
  • Erscheinungstermin: 19. November 2010
  • Englisch
  • Abmessung: 235mm x 155mm x 27mm
  • Gewicht: 738g
  • ISBN-13: 9781441918550
  • ISBN-10: 1441918558
  • Artikelnr.: 32457999
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
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
"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)