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Ibookroot October 20, 2007

Ibookroot October 20, 2007 fourier ANALYSISI bookroot October 20, 2007 PrincetonLecturesinAnalysisI fourier Analysis: An IntroductionII Complex AnalysisIII Real Analysis: Measure Theory, Integration, andHilbert SpacesIbookroot October 20, 2007 Princeton Lectures in AnalysisIFOURIER ANALYSISan introductionElias M. Stein&Rami ShakarchiPRINCETON UNIVERSITY PRESSPRINCETON AND OXFORDC opyright 2003 by Princeton University PressPublished by Princeton University Press, 41 William Street,Princeton, New Jersey 08540In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1 TWAll Rights ReservedLibrary of Congress Control Number 2003103688 ISBN 978-0-691-11384-5 British Library Cataloging-in-Publication Data is availableThe publisher would like to acknowledge the authors of this volume for providing the camera-ready copy from which this book was printedPrinted on acid-free paper.

Chapter 2. Basic Properties of Fourier Series 29 1 Examples and formulation of the problem 30 1.1 Main deflnitions and some examples 34 2 Uniqueness of Fourier series 39 3 Convolutions 44 4 Good kernels 48 5 Cesµaro and Abel summability: applications to Fourier series 51 5.1 Cesµaro means and summation 51 5.2 Fej¶er’s theorem 52

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