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We consider the inverse spectral problem for periodic Jacobi matrices interms of the vertical slits on the quasi-momentum domain plus the Dirichleteigenvalues, i.e., the Marchenko-Ostrovsky mapping. Moreover, we show that thegradients of the Dirichlet eigenvalues and of the so-called norming constantsare linear independent.

The parametrization of the Marchenko-Ostrovsky mapping in terms of the Dirichlet eigenvalues