
Complex Analysis
Conformal Inequalities and the Bieberbach Conjecture
Prem K. Kythe(Author)
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 28. November 2019
Book
Paperback/Softback
343 pages
978-0-367-44578-2 (ISBN)
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 Loewner 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 ?-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.
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 Loewner 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 ?-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.
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Professional Practice & Development
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 20 mm
Weight
553 gr
ISBN-13
978-0-367-44578-2 (9780367445782)
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Schweitzer Classification
Other editions
Additional editions

E-Book
04/2016
Chapman & Hall/CRC
€89.49
Available for download

E-Book
04/2016
Chapman and Hall
€89.99
Available for download

Book
12/2015
1st Edition
Chapman & Hall/CRC
€262.90
Shipment within 15-20 days
Person
Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/coauthor of 11 books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Green's functions, and coding theory.
Content
Analytic Functions. Univalent Functions. Area Principle. Loewner Theory. Higher-Order Coefficients. Subclasses of Univalent Functions. Generalized Convexity. Coefficients Estimates. Polynomials. De Branges Theorem. Epilogue: After de Branges. Appendices.