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arXiv · 2211.05029

Reduced transfer operators for singular difference equations

Hermann Schulz-Baldes
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Abstract

For tridiagonal block Jacobi operators, the standard transfer operator techniques only work if the off-diagonal entries are invertible. Under suitable assumptions on the range and kernel of these off-diagonal operators which assure a homogeneous minimal coupling between the blocks, it is shown how to construct reduced transfer operators that have the usual Krein space unitarity property and also a crucial monotonicity in the energy variable. This allows to extend the results of oscillation theory to such systems.

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Hermann Schulz-Baldes. 2022-11-09. Reduced transfer operators for singular difference equations. https://arxiv.org/abs/2211.05029

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