  We consider a third-order non-self-adjoint operator, which is an $L$-operator
in the Lax pair for the Boussinesq equation on the circle. We construct a
mapping from the set of operator coefficients to the set of spectral data,
similar to the corresponding mapping for the Hill operator constructed by E.
Korotyaev. We prove that in a neighborhood of zero our mapping is analytic and
one-to-one.
