An inverse nodal problem on semi-infinite intervals

by Wang, Tui-En

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


Date of Publication:07/07/2006

© 2009 All Rights Reserved.