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Scattering theory for difference equations with operator coefficients
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Scattering theory for difference equations with operator coefficients
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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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Cited by 1 Pith paper
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Factorization for the matrix-valued general Jacobi system on the full-line lattice
A factorization formula expresses the matrix-valued transmission and reflection coefficients for the full-line lattice in terms of the scattering coefficients for its left and right fragments.
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