Proof of the Bieberbach Conjecture for a Certain Class of Univalent Functions PDF Download

Author: Dov Aharonov
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 3

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Book Description

Author: Derek K. Thomas
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110560127
Category : Mathematics
Languages : en
Pages : 347

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Book Description
The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced researchers. Contents Univalent Functions – the Elementary Theory Definitions of Major Subclasses Fundamental Lemmas Starlike and Convex Functions Starlike and Convex Functions of Order α Strongly Starlike and Convex Functions Alpha-Convex Functions Gamma-Starlike Functions Close-to-Convex Functions Bazilevič Functions B1(α) Bazilevič Functions The Class U(λ) Convolutions Meromorphic Univalent Functions Loewner Theory Other Topics Open Problems

Author: P. L. Duren
Publisher: Springer Science & Business Media
ISBN: 9780387907956
Category : Mathematics
Languages : en
Pages : 414

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Book Description

Author: Sheng Gong
Publisher: American Mathematical Soc.
ISBN: 0821827421
Category : Education
Languages : en
Pages : 218

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Book Description
In 1919, Bieberbach posed a seemingly simple conjecture. That ``simple'' conjecture challenged mathematicians in complex analysis for the following 68 years! In that time, a huge number of papers discussing the conjecture and its related problems were inspired. Finally in 1984, de Branges completed the solution. In 1989, Professor Gong wrote and published a short book in Chinese, The Bieberbach Conjecture, outlining the history of the related problems and de Branges' proof. The present volume is the English translation of that Chinese edition with modifications by the author. In particular, he includes results related to several complex variables. Open problems and a large number of new mathematical results motivated by the Bieberbach conjecture are included. Completion of a standard one-year graduate complex analysis course will prepare the reader for understanding the book. It would make a nice supplementary text for a topics course at the advanced undergraduate or graduate level.

Author: Albert Baernstein (II)
Publisher: American Mathematical Soc.
ISBN: 0821815210
Category : Mathematics
Languages : en
Pages : 238

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Book Description
Louis de Branges of Purdue University is recognized as the mathematician who proved Bieberbach's conjecture. This book offers insight into the nature of the conjecture, its history and its proof. It is suitable for research mathematicians and analysts.

Author: Isaak Moiseevich Milin
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 216

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Book Description

Author: Mario Gonzalez
Publisher: Routledge
ISBN: 1351459376
Category : Mathematics
Languages : en
Pages : 552

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Book Description
A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

Author: Peter Henrici
Publisher: John Wiley & Sons
ISBN: 9780471589860
Category : Mathematics
Languages : en
Pages : 660

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Book Description
Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Author: Sanford S. Miller
Publisher: CRC Press
ISBN: 1482289814
Category : Mathematics
Languages : en
Pages : 481

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Book Description
"Examining a topic that has been the subject of more than 300 articles since it was first conceived nearly 20 years ago, this monograph describes for the first time in one volume the basic theory and multitude of applications in the study of differential subordinations."

Author: Anatoly Golberg
Publisher: Springer Nature
ISBN: 3031254244
Category : Mathematics
Languages : en
Pages : 319

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Book Description
Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.