Nine Introductions in Complex Analysis - Revised EditionElsevier, 10 d’oct. 2007 - 500 pàgines The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. - Proof of Bieberbach conjecture (after DeBranges) - Material on asymptotic values - Material on Natural Boundaries - First four chapters are comprehensive introduction to entire and metomorphic functions - First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off |
Continguts
| 1 | |
| 35 | |
Chapter 3 An Introduction to Entire Functions | 67 |
Chapter 4 Introduction to Meromorphic Functions | 107 |
Chapter 5 Asymptotic Values | 155 |
Chapter 6 Natural Boundaries | 189 |
Chapter 7 The Bieberbach Conjecture | 257 |
Chapter 8 Elliptic Functions | 297 |
Chapter 9 Introduction to the Riemann ZetaFunction | 397 |
Appendix | 451 |
| 473 | |
| 485 | |
Frases i termes més freqüents
Ahlfors analytic continuation analytic function analytic in B(0,1 angle argument asymptotic value Bieberbach Bieberbach conjecture bounded Chapter clearly coefficients compact subset complex number conformal mapping curve defined Definition Diagram Dirichlet series disk elliptic function entire function equation Example f is analytic f is entire f(re fact finite order formula function f function of finite fundamental parallelogram Furthermore given Hadamard Hence hypothesis inequality infinite integer inverse Jordan interior lattice point Let f(z line of Julia linear fractional transformation Loewner chain log M(r meromorphic function natural boundary neighborhood Nevanlinna non-constant Note O(log Picard's Pólya polynomial positive constant positive integer power series proof of Theorem radius of convergence real axis result Riemann Mapping Theorem Section sequence shows Similarly simple pole simply-connected region singular point Suppose f takes Theorem 2.1 upper half-plane w a lattice Weierstrass
Referències a aquest llibre
Elliptic Curves: Function Theory, Geometry, Arithmetic Henry McKean,Victor Moll Previsualització limitada - 1999 |