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      A study of the Hamburger moment problem on the real line

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      JINADU-THESIS-2017.pdf (362.1Kb)
      Date
      2017-09-18
      Author
      Jinadu, Ayoola Isaac 1991-
      ORCID
      0000-0001-9389-5824
      Type
      Thesis
      Degree Level
      Masters
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      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.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Kuhlmann, Salma
      Committee
      Samei, Ebrahim; Kusalik, Anthony; Bremner, Murray
      Copyright Date
      October 2017
      URI
      http://hdl.handle.net/10388/8097
      Subject
      Hamburger moment problem
      Borel measure
      positive definite sequence
      positive definite linear functionals, Hankel matrix, orthogonal polynomials
      Carleman's condition.
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