Approximation Theory and Harmonic Analysis on Spheres and Balls
This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the
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Feng Dai Yuan Xu
Approximation Theory and Harmonic Analysis on Spheres and Balls
Springer Monographs in Mathematics
For further volumes: http://www.springer.com/series/3733
Feng Dai • Yuan Xu
Approximation Theory and Harmonic Analysis on Spheres and Balls
123
Feng Dai Department of Mathematical and Statistical Sciences University of Alberta Edmonton, AB, Canada
Yuan Xu Department of Mathematics University of Oregon Eugene, OR, USA
ISSN 1439-7382 ISBN 978-1-4614-6659-8 ISBN 978-1-4614-6660-4 (eBook) DOI 10.1007/978-1-4614-6660-4 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013934217 Mathematics Subject Classification: 41Axx, 42Bxx, 42Cxx, 65Dxx © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is written as an introduction to analysis on the sphere and on the ball, and it provides a cohesive account of recent developments in approximation theory and harmonic analysis on these domains. Analysis on the unit sphere appears as part of Fourier analysis, in the study of homogeneous spaces, and in several fields in applied mathematics, from numerical analysis to geoscience, and it has seen increased activity in recent years. Its materials, however, are mostly
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