We give a report on the Sturm-Liouville problem defined on semi-infinite interval. Here as an extension of the Fourier expansion, we have a Parseval equality involving a Fourier integral with respect to a spectral function rho. This function rho is also related to Titchmarsh-Weyl m-function m(lambda) giving L2 solutions of the problem. The spectrum can be viewed as nonconstant points of the spectral function. Following Titchmarsh¡¦s monograph, we shall investigate the nature of the spectrum associated with different asymptotic behaviors of the potential function q, namely, when q¡÷¡Û, q¡÷0 or q¡÷-¡Û.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0723106-050528 |
| Date | 23 July 2006 |
| Creators | Lee, Shuo-Chi |
| Contributors | Wei-Cheng Lian, Tzon-Tzer Lu, Chun-Kong Law |
| 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-0723106-050528 |
| Rights | unrestricted, Copyright information available at source archive |
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