Paul J. Sally, Jr. (Chair)
2010 Mathematics Subject Classification. Primary 42-01.
Cover photo credit:
White Wall Mural by Joe St. Jean
Photographed by Leslie Patron
with permission of Chef Chris Nixon of Element 112, Sylvania, OH.
Page 267: “Young Heisenberg” by cartoonist/anthropolgist Emily Holt.
Reprinted with permission.
For additional information and updates on this book, visit
Library of Congress Cataloging-in-Publication Data
Montgomery, Hugh L., author.
Early Fourier analysis / Hugh L. Montgomery
pages cm. — (Pure and applied undergraduate texts ; volume 22)
Includes bibliographical references and index.
ISBN 978-1-4704-1560-0 (alk. paper)
1. Harmonic analysis. 2. Fourier transformations. I. Title.
Copying and reprinting. Individual readers of this publication, and nonprofit libraries
acting for them, are permitted to make fair use of the material, such as to copy select pages for
use in teaching or research. Permission is granted to quote brief passages from this publication in
reviews, provided the customary acknowledgment of the source is given.
Republication, systematic copying, or multiple reproduction of any material in this publication
is permitted only under license from the American Mathematical Society. Permissions to reuse
portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink
service. For more information, please visit: http://www.ams.org/rightslink.
Send requests for translation rights and licensed reprints to email@example.com.
Excluded from these provisions is material for which the author holds copyright. In such cases,
requests for permission to reuse or reprint material should be addressed directly to the author(s).
Copyright ownership is indicated on the copyright page, or on the lower right-hand corner of the
first page of each article within proceedings volumes.
c 2014 by the American Mathematical Society. All rights reserved.
The American Mathematical Society retains all rights
except those granted to the United States Government.
Printed in the United States of America.
∞ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.
Visit the AMS home page at http://www.ams.org/
10 9 8 7 6 5 4 3 2 1 19 18 17 16 15 14