Trace formulae for a class of Jacobi operators

The class of Jacobi operators generated by unit Borel measures with support formed by finitely many intervals of the real line $\mathbb R$ and finitely many points in $\mathbb R$ lying outside the convex hull of these intervals is investigated. An asymptotic formula for the diagonal Green's function in this class is obtained as well as the trace formulae for sequences $a,b\in\ell^\infty(\mathbb N)$ corresponding to a fixed operator.
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