Wavelets and
Multiwavelets
© 2004 by Chapman & Hall/CRC
, Studies in Advanced Mathematics
Titles Included in the Series
John P. D’Angelo, Several Complex Variables and the Geometry of Real Hypersurfaces
Steven R. Bell, The Cauchy Transform, Potential Theory, and Conformal Mapping
John J. Benedetto, Harmonic Analysis and Applications
John J. Benedetto and Michael W. Frazier, Wavelets: Mathematics and Applications
Albert Boggess, CR Manifolds and the Tangential Cauchy–Riemann Complex
Goong Chen and Jianxin Zhou, Vibration and Damping in Distributed Systems
Vol. 1: Analysis, Estimation, Attenuation, and Design
Vol. 2: WKB and Wave Methods, Visualization, and Experimentation
Carl C. Cowen and Barbara D. MacCluer, Composition Operators on Spaces of Analytic Functions
Jewgeni H. Dshalalow, Real Analysis: An Introduction to the Theory of Real Functions and Integration
Dean G. Duffy, Advanced Engineering Mathematics
Dean G. Duffy, Green’s Functions with Applications
Lawrence C. Evans and Ronald F. Gariepy, Measure Theory and Fine Properties of Functions
Gerald B. Folland, A Course in Abstract Harmonic Analysis
José García-Cuerva, Eugenio Hernández, Fernando Soria, and José-Luis Torrea,
Fourier Analysis and Partial Differential Equations
Peter B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem,
2nd Edition
Peter B. Gilkey, John V. Leahy, and Jeonghueong Park, Spectral Geometry, Riemannian Submersions,
and the Gromov-Lawson Conjecture
Alfred Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd Edition
Eugenio Hernández and Guido Weiss, A First Course on Wavelets
Kenneth B. Howell, Principles of Fourier Analysis
Fritz Keinert, Wavelets and Multiwavelets
Steven G. Krantz, The Elements of Advanced Mathematics, Second Edition
Steven G. Krantz, Partial Differential Equations and Complex Analysis
Steven G. Krantz, Real Analysis and Foundations
Steven G. Krantz, Handbook of Typography for the Mathematical Sciences
Kenneth L. Kuttler, Modern Analysis
Michael Pedersen, Functional Analysis in Applied Mathematics and Engineering
Clark Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, 2nd Edition
John Ryan, Clifford Algebras in Analysis and Related Topics
Xavier Saint Raymond, Elementary Introduction to the Theory of Pseudodifferential Operators
John Scherk, Algebra: A Computational Introduction
ÿ
Pavel Solín, Karel Segeth, and Ivo Doleÿzel, High-Order Finite Element Method
Robert Strichartz, A Guide to Distribution Theory and Fourier Transforms
André Unterberger and Harald Upmeier, Pseudodifferential Analysis on Symmetric Cones
James S. Walker, Fast Fourier Transforms, 2nd Edition
James S. Walker, A Primer on Wavelets and Their Scientific Applications
Gilbert G. Walter and Xiaoping Shen, Wavelets and Other Orthogonal Systems, Second Edition
Nik Weaver, Mathematical Quantization
Kehe Zhu, An Introduction to Operator Algebras
© 2004 by Chapman & Hall/CRC
, Wavelets and
Multiwavelets
FRITZ KEINERT
CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London New York Washington, D.C.
© 2004 by Chapman & Hall/CRC
, Library of Congress Cataloging-in-Publication Data
Keinert, Fritz.
Wavelets and multiwavelets / Fritz Keinert.
p. cm. — (Studies in advanced mathematics)
Includes bibliographical references and index.
ISBN 1-58488-304-9 (alk. paper)
1. Wavelets (Mathematics) I. Title. II. Series.
QA403.3.K45 2003
515¢.2433—dc22 2003055780
This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopying, microÞlming, and recording, or by any information storage or
retrieval system, without prior permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for
creating new works, or for resale. SpeciÞc permission must be obtained in writing from CRC Press LLC
for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identiÞcation and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com
© 2004 by Chapman & Hall/CRC
No claim to original U.S. Government works
International Standard Book Number 1-58488-304-9
Library of Congress Card Number 2003055780
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
© 2004 by Chapman & Hall/CRC
Multiwavelets
© 2004 by Chapman & Hall/CRC
, Studies in Advanced Mathematics
Titles Included in the Series
John P. D’Angelo, Several Complex Variables and the Geometry of Real Hypersurfaces
Steven R. Bell, The Cauchy Transform, Potential Theory, and Conformal Mapping
John J. Benedetto, Harmonic Analysis and Applications
John J. Benedetto and Michael W. Frazier, Wavelets: Mathematics and Applications
Albert Boggess, CR Manifolds and the Tangential Cauchy–Riemann Complex
Goong Chen and Jianxin Zhou, Vibration and Damping in Distributed Systems
Vol. 1: Analysis, Estimation, Attenuation, and Design
Vol. 2: WKB and Wave Methods, Visualization, and Experimentation
Carl C. Cowen and Barbara D. MacCluer, Composition Operators on Spaces of Analytic Functions
Jewgeni H. Dshalalow, Real Analysis: An Introduction to the Theory of Real Functions and Integration
Dean G. Duffy, Advanced Engineering Mathematics
Dean G. Duffy, Green’s Functions with Applications
Lawrence C. Evans and Ronald F. Gariepy, Measure Theory and Fine Properties of Functions
Gerald B. Folland, A Course in Abstract Harmonic Analysis
José García-Cuerva, Eugenio Hernández, Fernando Soria, and José-Luis Torrea,
Fourier Analysis and Partial Differential Equations
Peter B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem,
2nd Edition
Peter B. Gilkey, John V. Leahy, and Jeonghueong Park, Spectral Geometry, Riemannian Submersions,
and the Gromov-Lawson Conjecture
Alfred Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd Edition
Eugenio Hernández and Guido Weiss, A First Course on Wavelets
Kenneth B. Howell, Principles of Fourier Analysis
Fritz Keinert, Wavelets and Multiwavelets
Steven G. Krantz, The Elements of Advanced Mathematics, Second Edition
Steven G. Krantz, Partial Differential Equations and Complex Analysis
Steven G. Krantz, Real Analysis and Foundations
Steven G. Krantz, Handbook of Typography for the Mathematical Sciences
Kenneth L. Kuttler, Modern Analysis
Michael Pedersen, Functional Analysis in Applied Mathematics and Engineering
Clark Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, 2nd Edition
John Ryan, Clifford Algebras in Analysis and Related Topics
Xavier Saint Raymond, Elementary Introduction to the Theory of Pseudodifferential Operators
John Scherk, Algebra: A Computational Introduction
ÿ
Pavel Solín, Karel Segeth, and Ivo Doleÿzel, High-Order Finite Element Method
Robert Strichartz, A Guide to Distribution Theory and Fourier Transforms
André Unterberger and Harald Upmeier, Pseudodifferential Analysis on Symmetric Cones
James S. Walker, Fast Fourier Transforms, 2nd Edition
James S. Walker, A Primer on Wavelets and Their Scientific Applications
Gilbert G. Walter and Xiaoping Shen, Wavelets and Other Orthogonal Systems, Second Edition
Nik Weaver, Mathematical Quantization
Kehe Zhu, An Introduction to Operator Algebras
© 2004 by Chapman & Hall/CRC
, Wavelets and
Multiwavelets
FRITZ KEINERT
CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London New York Washington, D.C.
© 2004 by Chapman & Hall/CRC
, Library of Congress Cataloging-in-Publication Data
Keinert, Fritz.
Wavelets and multiwavelets / Fritz Keinert.
p. cm. — (Studies in advanced mathematics)
Includes bibliographical references and index.
ISBN 1-58488-304-9 (alk. paper)
1. Wavelets (Mathematics) I. Title. II. Series.
QA403.3.K45 2003
515¢.2433—dc22 2003055780
This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopying, microÞlming, and recording, or by any information storage or
retrieval system, without prior permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for
creating new works, or for resale. SpeciÞc permission must be obtained in writing from CRC Press LLC
for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identiÞcation and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com
© 2004 by Chapman & Hall/CRC
No claim to original U.S. Government works
International Standard Book Number 1-58488-304-9
Library of Congress Card Number 2003055780
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
© 2004 by Chapman & Hall/CRC
