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URN etd-0707106-122050
Author Tui-En Wang
Author's Email Address No Public.
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Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title An inverse nodal problem on semi-infinite intervals
Date of Defense 2006-06-15
Page Count 35
Keyword
  • inverse nodal problem
  • semi-infinite interval
  • reconstruction
  • Parseval's equation
  • singular Sturm-Liouville operator
  • Abstract The inverse nodal problem is the problem of understanding the potential
    function of the Sturm-Liouville operator from the set of the nodal data ( zeros of
    eigenfunction ). This problem was first defined by McLaughlin[12]. Up till now,
    the problem on finite intervals has been studied rather thoroughly. Uniqueness,
    reconstruction and stability problems are all solved.
    In this thesis, I investigate the inverse nodal problem on semi-infinite intervals
    q(x) is real and continuous on [0,1) and q(x)!1, as x!1. we have the
    following proposition. L is in the limit-point case. The spectral function  of the
    differential operator in (1) is a step function which has discontinuities at { k} ,
    k = 0, 1, 2, .... And the corresponding solutions (eigenfunction) k(x) = (x, k)
    has exactly k zeros on [0,1). Furthermore { k} forms an orthogonal set. Finally
    we also discuss that density of nodal points and a reconstruction formula on semiinfinite
    intervals.
    Advisory Committee
  • W. C. Lian - chair
  • Tzon-Tzer Lu - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0707106-122050.pdf
  • indicate in-campus access immediately and off_campus access in a year
    Date of Submission 2006-07-07

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