The parametrization of the Marchenko-Ostrovsky mapping in terms of the   Dirichlet eigenvalues
  We consider the inverse spectral problem for periodic Jacobi matrices in terms of the vertical slits on the quasi-momentum domain plus the Dirichlet eigenvalues, i.e., the Marchenko-Ostrovsky mapping. Moreover, we show that the gradients of the Dirichlet eigenvalues and of the so-called norming constants are linear independent. 
Maria Evgenievna Korotyaeva