Logarithmic Potentials with External Fields: Grundlehren der mathematischen Wissenschaften, cartea 316
Autor Edward B. Saff, Vilmos Totiken Limba Engleză Hardback – 9 oct 1997
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Specificații
ISBN-13: 9783540570783
ISBN-10: 3540570780
Pagini: 532
Ilustrații: XV, 505 p.
Dimensiuni: 155 x 235 x 34 mm
Greutate: 0.92 kg
Ediția:1997
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3540570780
Pagini: 532
Ilustrații: XV, 505 p.
Dimensiuni: 155 x 235 x 34 mm
Greutate: 0.92 kg
Ediția:1997
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
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.
Caracteristici
This book is devoted to the systematic mathematical study of the equilibrium problem of potential theory under the influence of an external field; as well as to its many-fold applications. The presentation not only serves as an introduction to the classical theory of logarithmic potentials, it provides a bridge to the frontiers of current research.
Notă biografică
Edward B. Saff received his B.S. in mathematics from the Georgia Institute of Technology and his Ph.D. from the University of Maryland, where he was a student of the renowned analyst Joseph L. Walsh. Saff’s research areas include approximation theory, numerical analysis, and potential theory. He has published more than 290 mathematical research articles, co-authored 9 books, and co-edited 11 volumes. Recognitions of his research include his election as a SIAM Fellow (Society for Industrial and Applied Mathematics) in 2023, as a Foreign Member of the Bulgarian Academy of Sciences in 2013, as a Fellow of the American Mathematical Society in 2013, as well as a Guggenheim Fellowship in 1978. Saff is co-Editor-in-Chief and Managing Editor of the research journal Constructive Approximation and serves on the editorial boards of Computational Methods and Function Theory and the Journal of Approximation Theory. He has mentored 18 Ph.D.’s as well as 13 post-docs. Saff is currently Distinguished Professor of Mathematics at Vanderbilt University.
Vilmos Totik was educated in Hungary and was a professor of mathematics at the University of Szeged and the University of South Florida until his retirement. His main research interest is classical mathematical analysis, approximation theory, orthogonal polynomials and potential theory. He has published (partially with co-authors) 5 monographs, one problem book in set theory and about 220 research papers in various disciplines.
Vilmos Totik was educated in Hungary and was a professor of mathematics at the University of Szeged and the University of South Florida until his retirement. His main research interest is classical mathematical analysis, approximation theory, orthogonal polynomials and potential theory. He has published (partially with co-authors) 5 monographs, one problem book in set theory and about 220 research papers in various disciplines.
Textul de pe ultima copertă
This is the second edition of an influential monograph on logarithmic potentials with external fields, incorporating some of the numerous advancements made since the initial publication.
As the title implies, the book expands the classical theory of logarithmic potentials to encompass scenarios involving an external field. This external field manifests as a weight function in problems dealing with energy minimization and its associated equilibria. These weighted energies arise in diverse applications such as the study of electrostatics problems, orthogonal polynomials, approximation by polynomials and rational functions, as well as tools for analyzing the asymptotic behavior of eigenvalues for random matrices, all of which are explored in the book. The theory delves into diverse properties of the extremal measure and its logarithmic potentials, paving the way for various numerical methods.
This new, updated edition has been thoroughly revised and is reorganized into three parts, Fundamentals, Applications and Generalizations, followed by the Appendices. Additions to the new edition include:
As the title implies, the book expands the classical theory of logarithmic potentials to encompass scenarios involving an external field. This external field manifests as a weight function in problems dealing with energy minimization and its associated equilibria. These weighted energies arise in diverse applications such as the study of electrostatics problems, orthogonal polynomials, approximation by polynomials and rational functions, as well as tools for analyzing the asymptotic behavior of eigenvalues for random matrices, all of which are explored in the book. The theory delves into diverse properties of the extremal measure and its logarithmic potentials, paving the way for various numerical methods.
This new, updated edition has been thoroughly revised and is reorganized into three parts, Fundamentals, Applications and Generalizations, followed by the Appendices. Additions to the new edition include:
- new material on the following topics: analytic and C² weights, differential and integral formulae for equilibrium measures, constrained energy problems, vector equilibrium problems, and a probabilistic approach to balayage and harmonic measures;
- a new chapter entitled Classical Logarithmic Potential Theory, which conveniently summarizes the main results for logarithmic potentials without external fields;
- several new proofs and sharpened forms of some main theorems;
- expanded bibliographic and historical notes with dozens of additional references.