On an inverse problem for finitedifference operators of second order
Abstract
The Jacobi matrices with bounded elements whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum are considered. A new type of spectral data, which are analogous for scattering data, is introduced for this matrix. An integral equation that allows us to reconstruct the matrix from this spectral data is obtained. We use this equation to solve the Cauchy problem for the Toda lattice with the initial data that are not stabilized.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110276
 Bibcode:
 2001math.....10276K
 Keywords:

 Spectral Theory;
 Mathematical Physics;
 35G25;
 34A15
 EPrint:
 47 pages