Lecons Sur les Familles Normales de Fonctions Analytiques et Leurs Applications (AMS Chelsea Publishing 271)

Lecons Sur les Familles Normales de Fonctions Analytiques et Leurs Applications (AMS Chelsea Publishing 271)

By: Paul Montel (author)Hardback

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Description

Most mathematicians first encounter normal families of functions through their application in the familiar proof of the Riemann mapping theorem. However, as this fine book demonstrates, normal families have many other roles to play in complex analysis. In particular, Montel covers normal families of meromorphic functions, holomorphic functions of several variables, systems of holomorphic functions, plus other interesting results about normal families of holomorphic functions of one variable. Along the way, Montel has interspersed some appealing proofs of sometimes familiar results, such as Borel's theorem on meromorphic functions and the Picard theorem. Although some of these methods have been supplanted by a more geometric point of view, it is worthwhile to get a glimpse of this older approach to complex analysis.

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Contents

Chapitre I: Ensembles de points. Familles de fonctions: Ensembles. Domaines Familles de fonctions Chapitre II: Fonctions holomorphes a valeurs exceptionnelles. Familles quasi-normales: Fonctions de Schwarz Familles de fonctions holomorphes a valeurs exceptionnelles Familles quasi-normales Chapitre III: Etude des fonctions uniformes autour d'un point essentiel isole Chapitre IV: Representation conforme: Representation conforme d'un domaine ouvert Correspondance entre les frontieres Chapitre V: Familles de fonctions meromorphes: Familles normales Familles quasi-normales Chapitre VI: Familles quasi-normales particulieres: Familles de fonctions a valeurs quasi-exceptionnelles Fonctions meromorphes exceptionnelles Chapitre VII: Suites de fonctions analytiques: Suites de fonctions holomorphes Suites de fonctions meromorphes Chapitre VIII: Iteration des fractions rationnelles Chapitre IX: Familles de fonctions de plusieurs variables: Familles normales de fonctions de deux variables Familles de fonctions uniformisantes Chapitre X: Familles complexes et applications: Familles complexes normales Familles complexes particulieres Fonctions algebroides admettant des involutions exceptionnelles Index.

Product Details

  • publication date: 15/01/1974
  • ISBN13: 9780828402712
  • Format: Hardback
  • Number Of Pages: 299
  • ID: 9780828402712
  • weight: 567
  • ISBN10: 082840271X
  • language of text: French

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