Montel''s Theorem, Mathematics

In 5 pages, please try to prove Theorem 3 based on Montel''s Theorem. please use "Latex" Knuth Donald to write this paper.

It is known that Theorem 3 on page 137 of the attached Krantz''s book would make a very nice "central result". In order to prove it, one needs in particular to have a good understanding of the topology of uniform convergence. As part of this, it is necessary to revise the detail of Montel''s Theorem (chapter one), since uniform convergence is intimately related to normal families of holomorphic functions. But another very important issue, not explicitly discussed by Krantz, is how the topology of uniform convergence relies on the assumption that any complex domain we are considering is a complete metric space.


Attached is
1- A plan for my thesis attached

2- Introduction

3- Some information about Theorem 3 with an important question that need to answered.

4- Krantz''s book, the main and important source for the thesis.

I need to keep up with an expert to finalise part of the thesis each week.
Posted Date: 9/15/2012 10:42:02 PM | Location : United States







Related Discussions:- Montel''s Theorem, Assignment Help, Ask Question on Montel''s Theorem, Get Answer, Expert's Help, Montel''s Theorem Discussions

Write discussion on Montel''s Theorem
Your posts are moderated
Related Questions
Please, I want to know and study "stability 0n predictor -corrector method .My gmail is thanhtutswe555@gmail.com.Please heap and kind to me .Thanks for this.

Rolle's Theorem  Assume f(x) is a function which satisfies all of the following. 1. f(x) is continuous in the closed interval [a,b]. 2. f(x) is differentiable in the ope

For this point we've only looked as solving particular differential equations. Though, many "real life" situations are governed through a system of differential equations. See the


Define an ordered rooted tree. Cite any two applications of the tree structure, also illustrate using an example each the purpose of the usage.   Ans: A  tree is a graph like t


The area of a rectangle is represented through the trinomial: x 2 + x - 12. Which of the subsequent binomials could represent the length and width? Because the formula for the

Submit your working in (neat) handwritten form (do not type up your solutions). For the plots that you generate in Maple or Matlab, you can print them out and attach them at the en


Calculate the slope of the line: Example: calculate  the  slope  of  the  line  whose  equation  is  y  =  2x  +  3  and  whose y-intercept is (0,3). Solution:    y =