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
The digraph D for a relation R on V = {1, 2, 3, 4} is shown below (a) show that (V,R) is a poset. (b) Draw its Hasse diagram. (c) Give a total order that have R.

tens digit of a 2-digit number is twice its unit digit. If the sum of the digit is 12, find the number.

what is the totel

Let A be an n×n matrix. Then Show that the set U = {u?R^n : Au = -3un} is a Subspace of R^n


The law of cosines can only be applied to acute triangles. Is this true or false?

NUMBER SYSTEMS: Numbers  are intellectual  witnesses  that belong  only  to  mankind. Example: If the H C F of 657 and 963 is expressible in the form of 657x + 963 x -

how do you divide

The given figure consists of four small semicircles and two big semicircles.  If the smaller semicircles are equal in radii and the bigger semicircles are also equal in radii, find

Inverse Cosine : Now see at inverse cosine.  Following is the definition for the inverse cosine.                         y = cos -1 x       ⇔ cos y = x                   for