Logarithmic Potentials with External Fields
In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techn
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Editors
S. S. Chern B. Eckmann P. de la Harpe H. Hironaka F. Hirzebruch N. Hitchin 1. Hormander M.-A. Knus A. Kupiainen J. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N. J. A. Sloane J.Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger J. Coates S.R.S. Varadhan
Springer-Verlag Berlin Heidelberg GmbH
Edward B. Saff . Vilmos Totik
Logarithmic Potentials with External Fields With 18 Figures
Springer-Verlag Berlin Heidelberg GmbH
Edward B. Saff
Vilmos rotik
University of South Florida Institute for Constructive Mathematics Department of Mathematics 4202 East Fowler Avenue, PHY 114 Tampa, FL 33620-5700, USA
Jozsef Attila University Bolyai Institute Aradi v. tere 1 Szeged, 6720 Hungary
[email protected]
[email protected] and U niversity of South Florida Department of Mathematics 4202 East Fowler Avenue, PHY 114 Tampa, FL 33620-5700, USA [email protected]
Library of Congress Cataloging-in-Publication Data Saff, E. B., 1944Logarithmic potentials with external fields / Edward B. Saff, Vilmos Totik. p. cm. - (Grundlehren der mathematischen Wissenschaften, ISSN 0072-7830; 316) Includes bibliographical references and index. (alk. paper) 1. Potential theory (Mathematics) I. Totik, V. II. Title. III. Series. QA404.7.S24 1997 515'.9-dc21 97-28048 CIP
Mathematics Subject Classification (1991): 31A15, 30C85, 41A17, 42A50, 33C25
ISSN 0072-7830 ISBN 978-3-642-08173-6 ISBN 978-3-662-03329-6 (eBook) DOI 10.1007/978-3-662-03329-6 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specificalIy 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 vers ion, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Softcover reprint of the hardcover 1st edition 1997 Cover design: MetaDesign plus GmbH, Berlin Typesetting: Authors' input files edited and reformatted by Kurt Mattes, Heidelberg, using a Springer TEX macro-package SPIN: 10124084 41/3143-5 4 3 2 1 o Printed on acid-free paper
To Loretta and Veronika
Preface
In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an extension of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and incl
