Similarities of discrete and continuous Sturm-Liouville problems
Texas State University-San Marcos, Department of Mathematics
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.
Green's function, Jacobi matrix, Sturm-Liouville equation, Eigenvalue, Eigenvector
Ghanbari, K. (2007). Similarities of discrete and continuous Sturm-Liouville problems. <i>Electronic Journal of Differential Equations, 2007</i>(172), pp. 1-8.
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