ON THE PARAMETRIZATION OF FINITE-GAP SOLUTIONS BY FREQUENCY AND WAVE-NUMBER VECTORS AND A THEOREM OF KRICHEVER,I

We discuss the parametrization of real finite-gap solutions of an inte grable equation by frequency and wavenumber vectors. This parametrizat ion underlies perturbation and averaging theories for the finite-gap s olutions. Out of the framework of integrable equations, the parametriz ation gives a convenient coordinate system on the corresponding manifo ld of Riemann curves.