Opis: Complex Analysis - Prem Kythe

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 Lowner 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 alpha-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.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 Lowner Theory Caratheodory's Kernel Theorem Lowner's Theorem Lowner-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 S0 Typically Real Functions Starlike Functions Functions with Real Coefficients Functions in Class Sa Generalized Convexity Convex Functions Close-to-Convex Functions gamma-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 Lowner Equations Lowner Curves Lowner 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.

Szczegóły: Complex Analysis - Prem Kythe

Tytuł: Complex Analysis
Autor: Prem Kythe
Producent: Productivity Press Inc
ISBN: 9781498718974
Rok produkcji: 2015
Ilość stron: 363
Oprawa: Twarda
Waga: 0.64 kg

Recenzje: Complex Analysis - Prem Kythe