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
three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of

Subjective Probability Probability may be determined by a personal statement of how likely an outcome is in a single trial or repetition of the same experiment. Since sub

Sample Space is the totality of all possible outcomes of an experiment. Hence if the experiment was inspecting a light bulb, the only possible outcomes

The sum of -4 and a number is equal to -48. What is the number? Let x = the number. Because sum is a key word for addition, the equation is -4 + x = -48. Add 4 to both sides o


The Mean Value Theorem for Integrals If  f (x ) is a continuous function on [a,b] then there is a number c in [a,b] such as,                                    ∫ b a f ( x

in a given figure a,b,c and d are points on a circle such that ABC =40 and DAB= 60 find the measure of DBA

Parametric Equations and Curves Till to this point we have looked almost completely at functions in the form y = f (x) or x = h (y) and approximately all of the formulas that w

Sharon needs to make 25 half-cup servings of soup. How many ounces of soup does she required? One cup is 8 ounces, so half a cup is 4 ounces. Multiply 25 by 4 ounces to find ou

Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of