Le grand théorème de Picard pour les multifonctions analytiques finies

• Autorzy: Bernard Aupetit , Mustapha Ech-Chérif El Kettani
• Języki publikacji: FR EN

Abstrakty

EN

Let D be a domain of the complex plane containing the origin. The famous great theorem of Émile Picard asserts that if h is holomorphic on D∖{0}, with an essential singularity at 0, then the image under h of any pointed neighbourhood of 0 covers all the complex plane, with at most one exception. Introducing the concept of essential singularity for analytic multifunctions, we extend this theorem to a finite analytic multifunction K, of degree N, defined on D∖{0}. In this case $⋃_{0<|λ|

Kategorie tematyczne

• 46Hxx: Topological algebras, normed rings and algebras, Banach algebras
• 32A12: Multifunctions
• 47Axx: General theory of linear operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2001
• Tom: 77
• Numer: 2
• Strony: 189-196

Daty

wydano

2001

Twórcy

autor

Bernard Aupetit

• Département de mathématiques, et de statistique, Faculté des sciences et de génie, Université Laval, Québec, Canada, G1K 7P4

autor

Mustapha Ech-Chérif El Kettani

• Département de mathématiques, et informatique, Faculté des sciences Dhar El-Mahraz, B.P. 1796 Atlas, Fès, Maroc

Identyfikatory

DOI

10.4064/ap77-2-5