Title page for etd-0630105-012021


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URN etd-0630105-012021
Author Chun-Jen Wu
Author's Email Address No Public.
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Department Applied Mathematics
Year 2004
Semester 2
Degree Master
Type of Document
Language English
Title Reconstruction formulas for periodic potential functions of Hill's equation using nodal data
Date of Defense 2005-06-03
Page Count 25
Keyword
  • Hill's equation
  • inverse nodal problems
  • periodic potential function
  • Reconstruction formula
  • nodal point
  • Abstract The Hill's equation is the Schrodinger equation $$-y'+qy=la y$$ with a periodic one-dimensional
    potential function $q$ and coupled with periodic boundary
    conditions $y(0)=y(1)$, $y'(0)=y'(1)$ or anti-periodic boundary conditions $y(0)=-y(1)$, $y'(0)=-y'(1)$.
    We study the inverse nodal problem for Hill's
    equation, in particular the reconstruction problem. Namely, we want to reconstruct the potential function using only nodal data ( zeros of eigenfunctions ). In this thesis, we give a reconstruction formula for $q$ using the periodic nodal data or using anti-periodic nodal data
    We show that the convergence is pointwise for all $x in (0,1)$ where $q$ is continuous; and pointwise for $a.e.$ $x in (0,1)$ as well as $L^1$ convergence when $qin L^1(0,1)$. We do this by making a translation so that the problem becomes a Dirichlet problem. The idea comes from the work of Coskun and Harris.
    Advisory Committee
  • Chiu-Ya Lan - chair
  • Wei-Cheng Lian - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0630105-012021.pdf
  • indicate access worldwide
    Date of Submission 2005-06-30

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