Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
This book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close
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Valery V. Volchkov
Vitaly V. Volchkov
Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
Prof. Valery V. Volchkov Mathematical Department Donetsk National University Donetsk 83001 Ukraine
Prof. Vitaly V. Volchkov Mathematical Department Donetsk National University Donetsk 83001 Ukraine
ISSN 1439-7382 ISBN 978-1-84882-532-1 e-ISBN 978-1-84882-533-8 DOI 10.1007/978-1-84882-533-8 Springer Dordrecht Heidelberg London New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2009925998 Mathematics Subject Classification (2000): 33C05, 33C10, 33C15, 33C45, 33C55, 33C80, 35P10, 42A38, 42A55, 42A65, 42A75, 42A85, 42B35, 42C30, 42C15, 43A32, 43A45, 43A85, 43A90, 44A12, 44A15, 44A20, 44A35, 45A05, 46F12, 53C35 c Springer-Verlag London Limited 2009 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local aspects of spectral analysis and spectral synthesis on homogeneous spaces. The study of these problems turns out to be closely related to a variety of questions in harmonic analysis, complex analysis, partial differential equations, integral geometry, approximation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active field of investigation at the moment. The simplest examples of symmetric spaces, the classical 2-sphere S2 and the hyperbolic plane H2 , play familiar roles in many areas in mathematics. The Heisenberg group H n is a principal model for nilpotent groups, and results obtaine
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