Periodic Jacobi operator with finitely supported perturbation on the halflattice
Abstract
We consider a periodic Jacobi operator J with finitely supported perturbations on the halflattice. We describe all eigenvalues and resonances of J and give their properties. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the Jost functions is onetoone and onto, we show how the Jost functions can be reconstructed from all eigenvalues, resonances and from the set of zeros of S(λ)  1, where S(λ) is the scattering matrix.
 Publication:

Inverse Problems
 Pub Date:
 November 2011
 DOI:
 10.1088/02665611/27/11/115003
 arXiv:
 arXiv:1004.2664
 Bibcode:
 2011InvPr..27k5003I
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics
 EPrint:
 29 pages