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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0707106-122050 |
| Date | 07 July 2006 |
| Creators | Wang, Tui-En |
| Contributors | Tzon-Tzer Lu, Chun-Kong Law, W. C. Lian |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0707106-122050 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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