In this talk I will present some recent results
on perturbations of almost-periodic Jacobi matrices with a
finite number of gaps in the spectrum. In particular, I will
discuss a Szego-type theorem which provides a description of
all Jacobi matrices with spectral measures satisfying a
Szego-type condition. I will also address a limit almost
periodic behavior of coefficients for such Jacobi matrices.

This talk is based on joint work in progress with Jacob
Christiansen and Barry Simon.