Multiscale, Nonlinear and Adaptive Approximation Dedicated to Wolfga
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Ronald A. DeVore
r
Angela Kunoth
Editors
Multiscale, Nonlinear and Adaptive Approximation Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday
Editors Ronald A. DeVore Department of Mathematics Texas A&M University College Station, TX 77840 USA [email protected]
Angela Kunoth Institut für Mathematik Universität Paderborn Warburger Str. 100 33098 Paderborn Germany [email protected]
ISBN 978-3-642-03412-1 e-ISBN 978-3-642-03413-8 DOI 10.1007/978-3-642-03413-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009935698 Mathematics Subject Classification (2000): 41-XX, 65-XX c Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, 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 protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday
Preface
On the occasion of his 60th birthday in October 2009, friends, collaborators, and admirers of Wolfgang Dahmen have organized this volume which touches on various of his research interests. This volume will provide an easy to read excursion into many important topics in applied and computational mathematics. These include nonlinear and adaptive approximation, multivariate splines, subdivision schemes, multiscale and wavelet methods, numerical schemes for partial differential and boundary integral equations, learning theory, and high-dimensional integrals. College Station, Texas, USA Paderborn, Germany June 2009
Ronald A. DeVore Angela Kunoth
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Acknowledgements
We are deeply grateful to Dr. Martin Peters and Thanh-Ha Le Thi from Springer for realizing this book project and to Frank Holzwarth for technical support.
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Contents
Introduction: Wolfgang Dahmen’s mathematical work . . . . . . . . . . . . . . . . 1 Ronald A. DeVore and Angela Kunoth 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The early years: Classical approximation theory . . . . . . . . . . . . . . . . 2 3 Bonn, Bielefeld, Berlin, and multivariate splines . . . . . . . . . . . . . . . 2 3.1 Computer aided geometric design . . . . . . . . . . . . . . .
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