# An inverse nodal problem on semi-infinite intervals

Abstract (Summary)

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.
Bibliographical Information:

Advisor:Tzon-Tzer Lu; Chun-Kong Law; W. C. Lian

School:National Sun Yat-Sen University

School Location:China - Taiwan

Source Type:Master's Thesis

Keywords:inverse nodal problem semi infinite interval reconstruction parseval s equation singular sturm liouville operator

ISBN:

Date of Publication:07/07/2006