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Title of Thesis

Algebraic Properties of Entire Functions with Coefficients in Particular Valued Fields

Author(s)

SARDAR MOHIB ALI KHAN

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2010
Subject
Mathematics
Number of Pages
86
Keywords (Extracted from title, table of contents and abstract of thesis)
Algebraic, Properties, Entire, Functions, Coefficients, Particular, Valued Fields, Polya, polynomials, function theory

Abstract
The study of entire functions is of central importance in complex function theory. We consider the ring of entire functions either on sub fields of C or on some sub fields of Cp: By using a technique based on admissible filters we study the ideal structure of the ring of entire functions. Then we prove the B ezout property for the ring of entire functions over Cp independent of Mittag-Le er theorem.
An important problem in complex function theory is to find an entire function from its values on a given sequence. By means of so-called Newton entire functions we solve a series of interpolation problems. Then we obtain a general result which implies the results of Polya and Gel'fond on the entire functions which are polynomials. We prove a similar result for the entire functions f such that f(D) D; where D is a particular bounded set. As an application we replace the use of power series for the initial value problems for ODE's with Newton series for boundary value problems.

Download Full Thesis
393 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

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2

1

PRELIMINARIES

1.1 Entire functions

1.2 Order and type of an entire function

1.3 Algebraic properties of entire functions

1.4 On the field Cp

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3 2 IDEAL STRUCTURE

2.1 Entire functions on Cp

2.2 Admissible filters

2.3 Free ideals of entire functions

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4 3 COMPLEX INTERPOLATION

3.1 Newton interpolating algebra

3.2 Newton entire functions

3.3 Interpolation problems

3.4 Arithmetic properties of Newton entire functions

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5 4 APPLICATIONS

4.1 Approximate Solutions of ODEs

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6 5 BIBLIOGRAPHY

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