Functions, Spaces, and Expansions Mathematical Tools in Physics and
This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outs
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Douglas Cochran Arizona State University
Ingrid Daubechies Princeton University
Hans G. Feichtinger University of Vienna
Christopher Heil Georgia Institute of Technology James McClellan Georgia Institute of Technology Michael Unser Swiss Federal Institute of Technology, Lausanne M. Victor Wickerhauser Washington University
Murat Kunt Swiss Federal Institute of Technology, Lausanne Wim Sweldens Lucent Technologies, Bell Laboratories Martin Vetterli Swiss Federal Institute of Technology, Lausanne
Ole Christensen
Functions, Spaces, and Expansions Mathematical Tools in Physics and Engineering
Birkhäuser Boston • Basel • Berlin
Ole Christensen Technical University of Denmark Department of Mathematics 2800 Lyngby Denmark [email protected]
ISBN 978-0-8176-4979-1 e-ISBN 978-0-8176-4980-7 DOI 10.1007/978-0-8176-4980-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010928840 Mathematics Subject Classification (2010): 40-01, 41-01, 42-01, 46-01 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Birkhäuser is part of Springer Science+Business Media (www.birkhauser.com)
ANHA Series Preface
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series reflects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as signal processing, partial differential equations (PDEs), and image processing is reflected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, tim
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