Comm. Math. Phys. 196-1, 175-202 (1998) [DOI: 10.1007/s002200050419]

Trace Formulas and Inverse Spectral Theory for Jacobi Operators

Gerald Teschl

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.

MSC91: Primary 39A10, 39A70; Secondary 34B20, 35Q58
Keywords: Trace formulas, Jacobi operators, inverse spectral theory, scattering theory

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