Harmonic Analysis, Signal Processing, and Complexity Festschrift in
Carlos A. Berenstein has had a profound influence on scholars and practitioners alike amid a distinguished mathematical career spanning nearly four decades. His uncommon capability of adroitly moving between these parallel worlds is demonstrated by the br
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Series Editors Hyman Bass Joseph Oesterle Alan Weinstein
Harmonic Analysis, Signal Processing, and Complexity Festschrift in Honor ofthe 60th Birthday of Carlos A. Berenstein
Irene Sabadini Daniele C. Struppa David F. Walnut Editors
Birkhauser Boston • Basel • Berlin
Daniele C. Struppa and David F. Walnut George Mason University Department of Mathematical Sciences Fairfax, VA 22030 U.S.A.
Irene Sabadini PoIitecnico di Milano Dipartimento di Matematica 1-20133 Milano Italy
AMS Subject Classifications (2000): Primary: 05C05, 05C50, 31C20, 32A26, 32A50, 35C15, 35N05, 35R30, 42A85, 42BI0, 42B35, 43A85, 44Al2, 46F12, 46F15, 65R30, 92C55, 94AI2
Library of Congress Cataloging-in-Publication Data Harmonic analysis, signal processing, and complexity: festschrift in honor of the 60th birthday of Carlos A. Berenstein / Irene Sabadini, Daniele C. Struppa, David F. Walnut, editors. p. cm. - (Progress in mathematics; v. 238) Includes bibliographical references. ISBN 0-8176-4358-3 (alk. paper) 1. Harmonic analysis-Congresses. 2. Signal processing-Congresses. 3. Computational complexity-Congresses. I. Berenstein, Carlos A. II. Sabadini, Irene (Irene Maria), 1965III. Struppa, Daniele Carlo, 1955- IV. Walnut, David F. V. Progress in mathematics (Boston, Mass.); v.238. QA403.H236 2005 515'.2433-dc22
2005045229
ISBN-IO 0-8176-4358-3 ISBN-13 978-0-8176-4358-4
e-IBSN 0-8176-4416-4
Printed on acid-free paper.
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©2005 Birkhauser Boston Birkhiiuser il{J?J All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhauser Boston, c/o Springer Science+Business Media Inc., 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 in the United States of America. 987654321
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SPIN 11008651
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Carlos A. Berenstein, sitting in front of Leonhard Euler's tomb in St. Petersburg, Russia.
Contents
Preface. . ... .. . .. . ... ... .. .. . .. . .. ... .. . .. ... .. ... ... .... ... .. .. Some Novel Aspects of the Cauchy Problem Leon Ehrenpreis
IX
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Analytic and Algebraic Ideas: How to Profit from Their Complementarity Alain Yger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
15
On Certain First-Order Partial Differential Equations in Cn Carlos A. Berenstein, Bao Qin Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 Hermite Operator on the Heisenberg Group Ovidiu Calin, Der-Chen Chang, Jingzhi Tie A Div-Curl Lemma in HMO on a Domain Der-
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