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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Logarithmic Potentials with External Fields
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Logarithmic Potentials with External Fields
Edward B. Saff, Vilmos Totik (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
08.12.2010
Sprache
Englisch
EAN
9783642081736
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Grundlehren der mathematischen Wissenschaften
Sonderedition
Nein
Autor
Edward B. Saff, Vilmos Totik
Seitenanzahl
505
Einbandart
Broschiert
Schlagwörter
Potential, Potential theory, analysis, approximation theory, capacity, external fields, extremal points, extremum problems, logarithmic potentials, orthogonal polynomials, rational functions, weighted polynomials
Thema-Inhalt
PBK - Mathematische Analysis, allgemein
TBJ - Mathematik für Ingenieure
PBW - Angewandte Mathematik
PHU - Mathematische Physik
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Spektrum, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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