Complex analysis : conformal inequalities and the Bieberbach conjecture /: conformal inequalities and the Bieberbach conjecture. (2015)

• Record Type: Book
• Further Information: Note: Prem K. Kythe.
• Authors: Kythe, Prem K
• Contents: Analytic Functions; Definitions; Jordan Contour; Cauchy–Riemann Equations; Line Integrals; Cauchy’s Theorems; Harmonic Functions; Piecewise Bounded Functions; Metric Spaces; Equicontinuity Univalent Functions ; Conformal Mapping; Some Theorems; Implications; Analytic Continuation; Schwarz Reflection Principle; Bilinear Transformation; Poisson’s Formula Area Principle ; Area Theorems; Bieberbach Conjecture; Lebedev–Milin’s Area Theorem; Koebe’s Theorem; Grunsky Inequalities; Polynomial Area Theorem; Distortion Theorems; Criterion for Univalency; Schwarzian Derivative Löwner Theory ; Carathéodory’s Kernel Theorem; Löwner’s Theorem; Löwner–Kufarev Equation; Applications; Slit Mappings Higher-Order Coefficients ; Variation Method; Fourth Coefficient; Grunsky Matrix ; Higher-Order Coefficients Subclasses of Univalent Functions ; Basis Classes; Functions with Positive Real Part; Functions in Class S 0 ; Typically Real Functions; Starlike Functions; Functions with Real Coefficients; Functions in Class S a Generalized Convexity ; Convex Functions; Close-to-Convex Functions; γ-Spiral Functions; Generalized Convexity; Alpha-Convex Functions Coefficients Estimates ; Mean Modulus; Hayman Index; Conformal Inequalities; Exponentiation of Inequalities Polynomials ; Orthogonal Polynomials; Hypergeometric Functions; Faber Polynomials De Branges Theorem ; Conjectures; de Branges Theorem; Alternate Proofs of de Branges Theorem; de Branges and Weinstein Systems of Functions Epilogue: After de Branges ; Chordal Löwner Equations; Löwner Curves; Löwner Chains in Cn; Multivariate Holomorphic Mappings; Beurling Transforms Appendix A: Mappings; Appendix B: Parametrized Curves; Appendix C: Green’s Theorems; Appendix D: Two-Dimensional Potential Flows; Appendix E: Subordination Principle Exercises appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 515.98; Functions of complex variables; Inequalities (Mathematics); Mathematical analysis
• Languages: English
• ISBNs: 9781498718998
• Related ISBNs: 9781498718974
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.