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arXiv · 2501.11194

Scattering theory for difference equations with operator coefficients

David Sher·Luis Silva·Boris Vertman·Monika Winklmeier
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Abstract

We consider a second order difference equation with operator-valued coefficients. More precisely, we study either compact or trace class perturbations of the discrete Laplacian in the Hilbert space of bi-infinite square-summable sequence with entries in a fixed Hilbert space. We discuss its continuous and discrete spectrum, as well as properties of the associated scattering matrix.

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David Sher, Luis Silva, Boris Vertman, Monika Winklmeier. 2025-01-19. Scattering theory for difference equations with operator coefficients. https://arxiv.org/abs/2501.11194

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