96-329 Gerald Teschl

Trace Formulas and Inverse Spectral Theory for Jacobi Operators (79K, LaTeX2e) Jul 5, 96

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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 an entirely 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.

Files: 96-329.tex