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URN etd-0612101-123650
Author Ya-ting Chen
Author's Email Address No Public.
Statistics This thesis had been viewed 5106 times. Download 1433 times.
Department Applied Mathematics
Year 2000
Semester 2
Degree Master
Type of Document
Language English
Title The Reconstruction Formula of Inverse
Nodal Problems and Related Topics
Date of Defense 2001-06-01
Page Count 23
Keyword
  • reconstruction formula
  • inverse nodal problem
  • Abstract Consider the Sturm-Liouville system :
    8 > > > > > < > > > > > :
    − y00 + q(x)y = y
    y(0) cos  + y0(0) sin  = 0
    y(1) cos  + y0(1) sin  = 0
    ,
    where q 2 L 1 (0, 1) and , 2 [0, ˇ).
    Let 0 < x(n)1 < x(n)2 < ... < x(n)n − 1 < 1 be the nodal points of n-th eigenfunction
    in (0,1). The inverse nodal problem involves the determination of the parameters
    (q, , ) in the system by the knowledge of the nodal points . This problem was
    first proposed and studied by McLaughlin. Hald-McLaughlin gave a reconstruc-
    tion formula of q(x) when q 2 C 1 . In 1999, Law-Shen-Yang improved a result
    of X. F. Yang to show that the same formula converges to q pointwisely for a.e.
    x 2 (0, 1), when q 2 L 1 .
    We found that there are some mistakes in the proof of the asymptotic formulas
    for sn and l(n)j in Law-Shen-Yang’s paper. So, in this thesis, we correct the
    mistakes and prove the reconstruction formula for q 2 L 1 again. Fortunately, the
    mistakes do not affect this result.Furthermore, we show that this reconstruction formula converges to q in
    L 1 (0, 1) . Our method is similar to that in the proof of pointwise convergence.
    Advisory Committee
  • Jhishen Tsay - chair
  • Chung-Tsun Shieh - co-chair
  • Chao-Nien Chen - co-chair
  • Tzy-Wei Hwang - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0612101-123650.pdf
  • indicate access worldwide
    Date of Submission 2001-06-12

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