Logarithmic Potentials with External Fields / by Edward B. Saff, Vilmos Totik
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 316)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 1997 |
| 本文言語 | 英語 |
| 大きさ | XV, 505 p : online resource |
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| 内容注記 | Preliminaries Weighted Potentials Recovery of Measures, Green Functions and Balayage Weighted Polynomials Determination of the Extremal Measure Extremal Point Methods Weights on the Real Line Applications Concerning Orthogonal Polynomials Signed Measures |
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| 一般注記 | 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 |
| 著者標目 | *Saff, Edward B. author Totik, Vilmos author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Functions of complex variables LCSH:Potential theory (Mathematics) LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Physics FREE:Mathematics FREE:Analysis FREE:Appl.Mathematics/Computational Methods of Engineering FREE:Applications of Mathematics FREE:Potential Theory FREE:Theoretical, Mathematical and Computational Physics FREE:Functions of a Complex Variable |
| 分 類 | DC23:515 |
| 巻冊次 | ISBN:9783662033296 
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| ISBN | 9783662033296 |
| URL | http://dx.doi.org/10.1007/978-3-662-03329-6 |
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