Fourier Analysis An Introduction (Princeton Lectures in Analysis, Volume 1) Elias M. Stein, Rami Shakarchi.pdf

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FOURIER ANALYSIS
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Princeton Lectures in Analysis
I Fourier Analysis: An Introduction
plex Analysis
III Real Analysis:
Measure Theory, Integration, and
Hilbert Spaces
Ibookroot October 20, 2007
Princeton Lectures in Analysis
I
FOURIER ANALYSIS
an introduction
Elias M. Stein
&
Rami Shakarchi
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright © 2003 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
6 Oxford Street, Woodstock, Oxfordshire OX20 1TW
All Rights Reserved
Library of Congress Control Number 2003103688
ISBN 978-0-691-11384-5
British Library Cataloging-in-Publication Data is available
The publisher would like to acknowledge the authors of this volume for
providing the camera-ready copy from which this book was printed
Printed on acid-free paper. ∞

Printed in the United States of America
5  7  9  10  8  6
Ibookroot October 20, 2007
To my grandchildren
Carolyn, Alison, Jason
.
To my parents
Mohamed & Mireille
and my brother
Karim
.
Ibookroot October 20, 2007
Foreword
Beginning in the spring of 2000, a series of four one-semester courses
were taught at Princeton University whose purpose was to present, in
an integrated manner, the core areas of analysis. The objective was to
make plain anic unity that exists between the various parts of the
subject, and to illustrate the wide applicability of ideas of analysis to
other fields of mathematics and science. The present series of books is
an elaboration of the lectures that were given.
While there are a number of excellent texts dealing with individual
parts of what we cover, our exposition aims at a different goal: pre-
senting the various sub-areas of analysis not as separate disciplines, but
rather as highly interconnected.