THE INVERSE PROBLEM FOR SELF-ADJOINT HANK EL-OPERATORS

We describe the self-adjoint operators on Hilbert space which are unit arily equivalent to a Hankel operator. A self-adjoint operator GAMMA i s unitarily equivalent to a Hankel operator if and only if GAMMA is no n-invertible, Ker GAMMA = {0} or dim Ker GAMMA = infinity, and its spe ctral multiplicity function nu satisfies the conditions: \nu(t)-nu(-t) \ less-than-or-equal-to = 2 on the absolutely continuous spectrum and \nu(t)-nu(-t)\ less-than-or-equal-to 1 on the singular spectrum.