 96329 Gerald Teschl
 Trace Formulas and Inverse Spectral Theory for Jacobi Operators
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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 selfcontained 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.
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96329.tex