

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 Kalgebra 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 padic analytic continuation by
means Newton interpolating series is presented.

