Harmonic Analysis on the Heisenberg Group
The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of ha
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Series Editors Hyman Bass Joseph Oesterle Alan Weinstein
Sundaram Thangavelu
Harmonie Analysis onthe
Heisenberg Group
Springer-Science+Business Media, LLC
Sundaram Thangavelu Indian Statistical Institute Statistics & Mathematics Division Bangalore 560 059 India
Ubrary of Congress Cataloging-in-Publication Data Thangavelu, Sundaram. Harmonie analysis on the Heisenberg group I Sundaram Thangavelu. p. cm. -- (Progress in mathematics ; v. 159) Includes bibliographical references and index. ISBN 978-1-4612-7275-5
ISBN 978-1-4612-1772-5 (eBook)
DOI 10.1007/978-1-4612-1772-5 1. Harmonie analysis. 2. Nilpotent Lie groups. I. Title. 11. Series: Progress in mathematics (Boston, Mass.) ; vol. 159. QA403.T53 1998 97-47315 515'.2433--dc21 CIP
AMS Codes: 43A30, 43A85, 43A90, 43A55, 43A50, 43A20, 43A15, 43AlO, 42B05, 42B08, 42B15, 42B20, 42B25, 22015, 22D20, 22E27 Printed on acid-free paper
© 1998 Springer Science+Business Media New York Originally published by Birkhäuser in 1998 Softcover reprint of the hardcover 1st edition 1998
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ISBN 978-1-4612-7275-5 Typeset by the author in TEX
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Preface
This monograph deals with various aspects of harmonic analysis on the Heisenberg group. The Heisenberg group is the most well known example from the realm of nilpotent Lie groups and plays an important role in several branches of mathematics, such as representation theory, partial differential equations, several complex variables and number theory. As it is the 'most commutative' among the noncommutative Lie groups, it offers the greatest opportunity for generalising the remarkable results of Euclidean harmonic analysis. My aim in this work is to demonstrate how standard results of abelian harmonic analysis, such as Plancherel and Paley-Wiener theorems, Wiener-Tauberian theorems, Bochner-Riesz means and multipliers for the Fourier transform, and so on, take shape in the noncommutative setup of the Heisenberg group. Basic results about the representations and the Fourier transform are covered in the first chapter. There are many good texts dealing with these basic results (see Folland [26]) but most of them stop there to develop differen
