Abstract:
Based on high energy expansions and Herglotz properties of Green and Weyl m-functions we develop a self-contained theory of trace formulas for Jacobi operators. In addition, we consider connections with inverse spectral theory, in particular uniqueness results. As an application we work out a new approach to the inverse spectral problem of a class of reflectionless operators producing explicit formulas for the coefficients in terms of minimal spectral data. Finally, trace formulas are applied to scattering theory with periodic backgrounds.
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Received: 5 November 1997 / Accepted: 27 January 1998
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Teschl, G. Trace Formulas and Inverse Spectral Theory for Jacobi Operators . Comm Math Phys 196, 175–202 (1998). https://doi.org/10.1007/s002200050419
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DOI: https://doi.org/10.1007/s002200050419