Abstract Harmonic Analysis Volume II: Structure and Analysis for Com
This book is a continuation of Volume I of the same title [Grund lehren der mathematischen Wissenschaften, Band 115 ]. We constantly 1 1. The textbook Real and cite definitions and results from Volume abstract analysis by E. HEWITT and K. R. STROMBERG [B
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Editors
M. Artin S.S. Chern J.M. Frohlich E. Heinz H. Hironaka F. Hirzebruch L. Hormander S. Mac Lane C.C. Moore J.K. Moser M. Nagata W. Schmidt D.S. Scott Ya.G. Sinai J. Tits B.L. van der Waerden M. Waldschmidt S. Watanabe Managing Editors
M. Berger B. Eckmann S.R.S. Varadhan
Edwin Hewitt
Kenneth A. Ross
Abstract Hartnonic Analysis Volume II Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups
Springer-Verlag Berlin Heidelberg GmbH
Edwin Hewitt Department of Mathematics GN-50 University of Washington Seattle, WA 98195, USA Kenneth A. Ross Department of Mathematics University of Oregon Eugene, OR 97403, USA
Second Reprint 2002
ISBN 978-3-662-24595-8 ISBN 978-3-662-26755-4 (eBook) DOI 10.1007/978-3-662-26755-4
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© Springer-Verlag Berlin Heidelberg 1970 Originally published by Springer-Verlag Berlin Heidelberg New York in 1970 41/3140-5 4 3 2 -Printed on acid-free paper SPIN 10874972
Dem Andenken John von Neumanns gewidmel
Preface This book is a continuation of Volume I of the same title [Grundlehren der mathematischen Wissenschaften, Band 115 ]. We constantly cite definitions and results from Volume 1.1 The textbook Real and abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin · Gottingen ·Heidelberg: Springer-Verlag 1965], which appeared between the publication of the two volumes of this work, contains many standard facts from analysis. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA. Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. We deal with general locally compact groups only where they are the natural setting for what we are considering, or where one or another group provides a useful counterexample. Readers who are interested only in compact groups may read as follows: § 27, Appendix D, §§ 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), §§ 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: §§ 31-33, 39-42, selected Miscellaneous Theorems and Examples in §§34-38. For all readers, § 43 is interesting but optional. Obviously we have not been able to cover all of harmonic analysis. The field, already immense, is growing rapidly at the present day. We were limited
