The spectral distribution and the inverse eigenvalue problem for the discontinuous Sturm-Liouville operators
WEI Zhaoying1,2, WEI Guangsheng1*
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China;2 College of Science, Xi′an Shiyou University, Xi′an 710065, Shaanxi, China)
Abstract:
The eigenvalue and the inverse eigenvalue problems of the Sturm-Liouville operators defined respectively on\[0,1\] \[0,t0\] and \[t0,1\] are considered. By using the monotonicity of the Weyl-Titchmarsh-m- function, it is shown that the three spectra are alternate, and the potential q(x) and the parameters h,H in the boundary conditions can be uniquely determined by the three spectra if the spectra of the operators defined on subintervals are disjoint.
KeyWords:
Sturm-Liouville operator; jump condition; eigenvalue; function of Herglotz; the inverse eigenvalue problem
