Logarithmic Potentials with External Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1997
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
316 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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 |
| Beschreibung: | 1 Online-Ressource (XV, 505 p) |
| ISBN: | 9783662033296 9783642081736 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-03329-6 |
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| 500 | |a 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 | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-03329-6 |
| format | Electronic eBook |
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| isbn | 9783662033296 9783642081736 |
| issn | 0072-7830 |
| language | English |
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| spelling | Saff, Edward B. Verfasser aut Logarithmic Potentials with External Fields by Edward B. Saff, Vilmos Totik Berlin, Heidelberg Springer Berlin Heidelberg 1997 1 Online-Ressource (XV, 505 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 316 0072-7830 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 Mathematics Functions of complex variables Potential theory (Mathematics) Potential Theory Theoretical, Mathematical and Computational Physics Functions of a Complex Variable Mathematik Logarithmisches Potenzial (DE-588)4168046-7 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Logarithmisches Potenzial (DE-588)4168046-7 s 1\p DE-604 Potenzialtheorie (DE-588)4046939-6 s 2\p DE-604 Totik, Vilmos Sonstige oth https://doi.org/10.1007/978-3-662-03329-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Saff, Edward B. Logarithmic Potentials with External Fields Mathematics Functions of complex variables Potential theory (Mathematics) Potential Theory Theoretical, Mathematical and Computational Physics Functions of a Complex Variable Mathematik Logarithmisches Potenzial (DE-588)4168046-7 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4168046-7 (DE-588)4046939-6 |
| title | Logarithmic Potentials with External Fields |
| title_auth | Logarithmic Potentials with External Fields |
| title_exact_search | Logarithmic Potentials with External Fields |
| title_full | Logarithmic Potentials with External Fields by Edward B. Saff, Vilmos Totik |
| title_fullStr | Logarithmic Potentials with External Fields by Edward B. Saff, Vilmos Totik |
| title_full_unstemmed | Logarithmic Potentials with External Fields by Edward B. Saff, Vilmos Totik |
| title_short | Logarithmic Potentials with External Fields |
| title_sort | logarithmic potentials with external fields |
| topic | Mathematics Functions of complex variables Potential theory (Mathematics) Potential Theory Theoretical, Mathematical and Computational Physics Functions of a Complex Variable Mathematik Logarithmisches Potenzial (DE-588)4168046-7 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Mathematics Functions of complex variables Potential theory (Mathematics) Potential Theory Theoretical, Mathematical and Computational Physics Functions of a Complex Variable Mathematik Logarithmisches Potenzial Potenzialtheorie |
| url | https://doi.org/10.1007/978-3-662-03329-6 |
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