Electron. J. Diff. Eqns., Vol. 2007(2007), No. 172, pp. 1-8.

Similarities of discrete and continuous Sturm-Liouville problems

Kazem Ghanbari

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 6, 2007.
Math Subject Classifications: 15A18, 15A24, 34B25, 34B27.
Key Words: Green's function; Jacobi matrix; Sturm-Liouville 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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