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# Periodic Jacobi operator with finitely supported perturbations: the inverse resonance problem

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 Publication Article, other scientific Title Periodic Jacobi operator with finitely supported perturbations: the inverse resonance problem Author ; Date 2011 English abstract We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of the transmission coefficient and the Jost function on the right half-axis, is one-to-one and onto. We consider the problem of reconstruction of the scattering data from all eigenvalues, resonances and the set of zeros of $R_-(\lambda)+1,$ where $R_-$ is the reflection coefficient. Link http://arxiv.org/abs/1105.3397 (external link to publication) Host/Issue Arxiv.org; Language eng (iso) Subject JacobiresonancesperiodicSciencesResearch Subject Categories::MATHEMATICS Handle http://hdl.handle.net/2043/12064 Permalink to this page
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