Abstract
We study discrete Schrödinger operators with compactly supported potentials on Z d. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely reconstructed from the S-matrix of all energies. We also study the spectral shift function \({\xi(\lambda)}\) for the trace class potentials, and estimate the discrete spectrum in terms of the moments of \({\xi(\lambda)}\) and the potential.
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Communicated by Jan Derezinski.
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Isozaki, H., Korotyaev, E. Inverse Problems, Trace Formulae for Discrete Schrödinger Operators. Ann. Henri Poincaré 13, 751–788 (2012). https://doi.org/10.1007/s00023-011-0141-0
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DOI: https://doi.org/10.1007/s00023-011-0141-0