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Title of Thesis

On the Algebra of Newton Interpolating Series and its Applications

Author(s)

AZEEM HAIDER

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2010
Subject
Mathematics
Number of Pages
87
Keywords (Extracted from title, table of contents and abstract of thesis)
Algebra, Newton, Interpolating, Series, Applications, sequence, analytic, continuation

Abstract
By means of a sequence S of elements of a eld K; we de ned a K-algebra KS[[X]] of formal series called Newton interpolating series which generalized the formal power series. We study algebraic properties of this algebra and in the case when S has a nite number of distinct elements we prove that it is isomorphic to a direct sum of a nite number of known algebras. A representation of strictly convergent power series as convergent Newton interpolating series is given. Then this representation is used to study problems of the zeros of strictly convergent power series and to solve an interpolation problem. We also study the problem of the zeros of bounded Newton interpolating series. A method for p-adic analytic continuation by means Newton interpolating series is presented.

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417 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

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2

1

PRELIMINARIES

1.1 Ring of formal power series

1.2 Topological rings and absolute value

1.3 Tate algebra

1.4 Mahler series

1.5 p-adic analytic elements

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3 2 NEWTON INTERPOLATING SERIES

2.1 Definitions and notations

2.2 Algebraic properties

2.3 Structure of the ring KS[[X]]

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4 3 NEWTON INTERPOLATING SERIES IN N INDETERMINATES

3.1 Definitions and notations

3.2 A representation of strictly convergent power series

3.3 Applications

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5 4 BOUNDED NEWTON INTERPOLATING SERIES

4.1 Representation theorem and analytic properties

4.2 Zeros of bounded Newton interpolating series

4.3 Continuous functions and bounded Newton interpolating series

4.4 Newton analytic elements

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6 5 BIBLIOGRAPHY

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