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Perturbed discrete Sturm-Liouville problems and associated sampling theorems. (English) Zbl 1191.39004

The aim of the paper is to investigate spectral properties of perturbed second-order difference operators. The underlying eigenvalue problem has the form
\[ \nabla[p(n)\Delta y(n)]+ q(n)y(n)+ \sum_{i=1}^N r(n) r(i) y(i)= \lambda y(n). \]
In a sequence of lemmata the authors present results about selfadjointness, Green’s function, uniqueness of solutions, multiplicity of eigenvalues, eigenfunction expansion, sampling representations. In a final section some examples illustrate the results.

MSC:

39A12 Discrete version of topics in analysis
39A70 Difference operators
94A20 Sampling theory in information and communication theory
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
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