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Transformations of difference equations. II. (English) Zbl 1202.39001

Summary: This is an extension of the work done by the authors [Adv. Difference Equ. 2010, Article ID 947058, 22 p. (2010; Zbl 1198.39001)] where we studied the effect of applying two Crum-type transformations to a weighted second-order difference equation with non-eigenparameter-dependent boundary conditions at the end points. In particular, we now consider boundary conditions which depend affinely on the eigenparameter together with various combinations of Dirichlet and non-Dirichlet boundary conditions. The spectra of the resulting transformed boundary value problems are then compared to the spectra of the original boundary value problems.

MSC:

39A05 General theory of difference equations

Citations:

Zbl 1198.39001
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References:

[1] Currie, S; Love, A, Transformations of difference equations I, 22, (2010) · Zbl 1198.39001
[2] Atkinson FV: Discrete and Continuous Boundary Problems, Mathematics in Science and Engineering, vol. 8. Academic Press, New York, NY, USA; 1964:xiv+570.
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