Approximation of infinite-zone potentials by finite-zone potentials

In this paper it is proved that each infinite-zone potential of the class considered in the paper “Almost periodicity of infinite-zone potentials” (Izv. Akad. Nauk SSSR Ser. Mat., 1981, v. 45, № 2, pp. 291–320) is the uniform limit of finite-zone potentials on the entire real line. The proof is based on a detailed study of the problem of Jacobi inversion on a two-sheeted Riemann surface with an infinite number of branch points.
Bibliography: 5 titles.