The nature of spectrum for some singular Sturm-Liouville operators

• Main Authors: Shuo-Chi Lee, 李碩祈
• Other Authors: Chun-Kong Law
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/07897585388516090550

碩士 === 國立中山大學 === 應用數學系研究所 === 94 === 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→∞, q→0 or q→-∞.