Anand J Antony , M Krishna.
Inverse spectral theory for Jacobi matrices and their
almost periodicity
(125K, LaTex)
ABSTRACT. In this paper we consider the inverse problem for bounded Jacobi matrices
with nonempty absolutely continuous spectrum and as an application show the
almost periodicity of some random Jacobi matrices. We do the inversion in
two different ways. In the general case we use a direct method of
reconstructing the Green functions. In the special case where we show
the almost periodicity, we use an alternative method using the trace formula
for points in the
orbit of the matrices under translations. This method of reconstruction
involves analyzing the Abel-Jacobi map and solving of the Jacobi inversion
problem associated with an infinite genus Riemann surface constructed from
the spectrum.