The finite section method for infinite Vandermonde matrices and applications

Abstract

In this thesis we investigate a very well known and relevant question, i.e, to solve a linear equation Ax = b, where A and b are given. In our study A denotes an infinite matrix of special form called a Vandermonde matrix and b will be a vector from a given sequence space. We will consider two cases of the equation above. Different constraints will be placed upon the entries of A and b will be chosen from different sequence spaces. We will also look at an example from the first case to show how the theory can be applied. Our approach to solving this equation will be to apply the Finite Section Method. Here we follow the exposition of [9] while clarifying and explaining their approach. In addition, we will draw on various mathematical fields to assist our investigation. These include linear algebra, functional analysis, operator theory, complex analysis and topological vector spaces.