A study of the Hamburger moment problem on the real line
Date
2017-09-18
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0001-9389-5824
Type
Thesis
Degree Level
Masters
Abstract
This thesis contains an exposition of the Hamburger moment problem. The Hamburger moment problem is an interesting question in analysis that deals with finding the existence of a Borel measure representing a given positive semi-definite linear functional. We begin our exposition by constructing orthogonal polynomials associated with a positive definite sequence. Then we discuss the interlacing property of the zeros of these orthogonal polynomials. We proceed by finding a solution to the truncated Hamburger moment problem and then extend the found solution to the complete Hamburger moment problem. After obtaining a solution to the Hamburger moment problem, we address the problem of determinacy of the moment problem. Finally, we discuss a result that proves the density of polynomials with complex coefficients under the assumption that the Carleman's condition is satisfied.
Description
Keywords
Hamburger moment problem, Borel measure, positive definite sequence, positive definite linear functionals, Hankel matrix, orthogonal polynomials, Carleman's condition.
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Mathematics