Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 172, pp. 18.
Similarities of discrete and continuous SturmLiouville problems
Kazem Ghanbari
Abstract:
In this paper we present a study on the analogous properties
of discrete and continuous SturmLiouville 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
mfunction determines the SturmLiouville operators
uniquely. Moreover, the well known RayleighRitz Theorem in
linear algebra can be proved by using the concept of Green's
function in discrete case.
Submitted November 7, 2006. Published December 6, 2007.
Math Subject Classifications: 15A18, 15A24, 34B25, 34B27.
Key Words: Green's function; Jacobi matrix; SturmLiouville equation;
eigenvalue; eigenvector.
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Kazem Ghanbari
Department of Mathematics
Sahand University of Technology, Tabriz, Iran
email: kghanbari@sut.ac.ir 
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