Logarithmic Potentials with External Fields

Edward B. Saff

ISBN 10: 3642081738 / ISBN 13: 9783642081736

Published by Springer, Springer Dez 2010, 2010

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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 exten sion 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 includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the 'l/9-th' conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned 'weighted' potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 528 pp. Englisch.

Seller Inventory # 9783642081736

Bibliographic Details

• Title: Logarithmic Potentials with External Fields
• Publisher: Springer, Springer Dez 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 3642081738
• ISBN 13: 9783642081736
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 29D millimeters 235 millimeters width by 155 millimeters height by 29 millimeters depth
• Weight: 791 grams

About this title

Synopsis

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 exten­ sion 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 includes: creation of the theory of non-classical orthogonal polynomials with re­ spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.