Compactness and Convergence in the Space of Analytic Functions
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Date
2011-01
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Addis Ababa University
Abstract
This project is a reading material in all Complx Analysis. it deals mainly with the class
of Analytic Functions on an open set G.
Our purpose is to desc ribe this class of analytic functions is complete metric space with
dclincd metric space. As a consequence we prove the SCI of all continuous function is
com plete metric space.
Let 'F be family of analytic function in a region G. We prove that 'F is a normal
famiey.
provided that 'F is loca lly bounded.
We also briefly discuss applications to the normal families of analytic func tions
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Keywords
Space of Analytic Functions