Inequalities: Theory of Majorization and Its Applications
This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most
- PDF / 7,019,240 Bytes
- 919 Pages / 439 x 666 pts Page_size
- 103 Downloads / 209 Views
For other titles published in this series, go to http://www.springer.com/series/692
Albert W. Marshall Barry C. Arnold
•
Ingram Olkin
Inequalities: Theory of Majorization and Its Applications Second Edition
ABC
Albert W. Marshall Department of Statistics University of British Columbia Vancouver, BC V6T 1Z2 Canada and mailing address 2781 W. Shore Drive Lummi Island, WA 98262 [email protected]
Barry C. Arnold Department of Statistics University of California Riverside, CA 92521 USA [email protected]
Ingram Olkin Department of Statistics Stanford University Stanford, CA 94305 USA [email protected]
ISSN 0172-7397 ISBN 978-0-387-40087-7 ISBN 978-0-387-68276-1 (eBook) DOI 10.1007/978-0-387-68276-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010931704 c Springer Science+Business Media, LLC 2011 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 Springer is part of Springer Science+Business Media (www.springer.com)
To our long-suffering wives for their patience with this project: Sheila (AWM), Anita (IO), Carole (BCA)
To the memory of Z.W. (Bill) Birnbaum and Edwin Hewitt who initiated my interest in inequalities (AWM)
To my students and colleagues who have energized, enriched and enlivened my life (IO)
To the memory of Peggy Franklin (BCA)
Preface and Acknowledgments from the First Edition
Preface Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying “theory of inequalities.” For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations. As the 1960s progressed, we became more and more aware of these facts. Our awareness was reinforced by a series of seminars we gave while visiting the University of Cambridge in 1967–1968. Because the ideas associated with majorization deserve to be better known, we decided by 1970 to write a little monograph on the subject—one that might have as many as 100 pages—and that was the genesis of this book. The idea of majorization is a s
Data Loading...
