URN 
etd0630105012021 
Author 
ChunJen Wu 
Author's Email Address 
No Public. 
Statistics 
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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 
20050603 
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 onedimensional potential function $q$ and coupled with periodic boundary conditions $y(0)=y(1)$, $y'(0)=y'(1)$ or antiperiodic 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 antiperiodic 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 
ChiuYa Lan  chair
WeiCheng Lian  cochair
ChunKong Law  advisor

Files 
indicate access worldwide 
Date of Submission 
20050630 