Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 172, pp. 1-8.

Title: Similarities of discrete and continuous Sturm-Liouville problems

Author: Kazem Ghanbari (Sahand Univ. of Technology, Tabriz, Iran)

Abstract: 
 In this paper we present a study on the analogous properties
 of discrete and continuous Sturm-Liouville problems arising in
 matrix analysis and differential equations, respectively. Green's
 functions in both cases have analogous expressions in terms of the
 spectral data. Most of the results associated to inverse problems
 in both cases are identical. In particular, in both cases Weyl's
 m-function determines the Sturm-Liouville operators
 uniquely. Moreover, the well known  Rayleigh-Ritz Theorem in
 linear algebra can be proved by using the concept of Green's
 function in discrete case.
 
Submitted November 7, 2006. Published December 06, 2007.
Math Subject Classifications: 15A18, 15A24, 34B25, 34B27.
Key Words: Green's function; Jacobi matrix; Sturm-Liouville equation; 
           eigenvalue; eigenvector.