Direct and inverse spectral problems for a class of non-self-adjoint periodic tridiagonal matrices

The spectral properties of a class of tridiagonal matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The obtained results extend some results on the direct and inverse spectral problems for periodic Jacobi matrices and for some non-self-adjoint tridiagonal matrices.