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Complex analysis: conformal inequalities and the Bieberbach conjecture

Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functi...

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Detalles Bibliográficos
Autor principal: Kythe, Prem K
Lenguaje:eng
Publicado: CRC Press 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1201/b19047
http://cds.cern.ch/record/2162156
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author Kythe, Prem K
author_facet Kythe, Prem K
author_sort Kythe, Prem K
collection CERN
description Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. Assuming basic knowledge of complex analysis and differential equations, the book is suitable for graduate students engaged in analytical research on the topics and researchers working on related areas of complex analysis in one or more complex variables. The author first reviews the theory of analytic functions, univalent functions, and conformal mapping before covering various theorems related to the area principle and discussing Löwner theory. He then presents Schiffer’s variation method, the bounds for the fourth and higher-order coefficients, various subclasses of univalent functions, generalized convexity and the class of a-convex functions, and numerical estimates of the coefficient problem. The book goes on to summarize orthogonal polynomials, explore the de Branges theorem, and address current and emerging developments since the de Branges theorem.
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spelling cern-21621562021-04-21T19:39:38Zdoi:10.1201/b19047http://cds.cern.ch/record/2162156engKythe, Prem KComplex analysis: conformal inequalities and the Bieberbach conjectureMathematical Physics and MathematicsComplex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. Assuming basic knowledge of complex analysis and differential equations, the book is suitable for graduate students engaged in analytical research on the topics and researchers working on related areas of complex analysis in one or more complex variables. The author first reviews the theory of analytic functions, univalent functions, and conformal mapping before covering various theorems related to the area principle and discussing Löwner theory. He then presents Schiffer’s variation method, the bounds for the fourth and higher-order coefficients, various subclasses of univalent functions, generalized convexity and the class of a-convex functions, and numerical estimates of the coefficient problem. The book goes on to summarize orthogonal polynomials, explore the de Branges theorem, and address current and emerging developments since the de Branges theorem.CRC Pressoai:cds.cern.ch:21621562015
spellingShingle Mathematical Physics and Mathematics
Kythe, Prem K
Complex analysis: conformal inequalities and the Bieberbach conjecture
title Complex analysis: conformal inequalities and the Bieberbach conjecture
title_full Complex analysis: conformal inequalities and the Bieberbach conjecture
title_fullStr Complex analysis: conformal inequalities and the Bieberbach conjecture
title_full_unstemmed Complex analysis: conformal inequalities and the Bieberbach conjecture
title_short Complex analysis: conformal inequalities and the Bieberbach conjecture
title_sort complex analysis: conformal inequalities and the bieberbach conjecture
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1201/b19047
http://cds.cern.ch/record/2162156
work_keys_str_mv AT kythepremk complexanalysisconformalinequalitiesandthebieberbachconjecture