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Deficiency indices and spectrum of fourth-order difference equations with unbounded coefficients. (English) Zbl 1264.39018

Authors’ abstract: Using subspace theory together with appropriate smoothness and decay conditions, we calculate the deficiency indices and absolutely continuous spectrum of fourth-order difference equations with unbounded coefficients. In particular, we find the absolutely continuous spectrum to be \(\mathbb R\) with a spectral multiplicity one.

MSC:

39A45 Difference equations in the complex domain
39A20 Multiplicative and other generalized difference equations
47A55 Perturbation theory of linear operators
39A10 Additive difference equations
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