Geodesic
Approximation of infinite-zone potentials by finite-zone potentials
Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 55-87.

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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. 
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B. M. Levitan. Approximation of infinite-zone potentials by finite-zone potentials. Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 55-87. http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a3/

[1] Levitan B. M., “Pochti periodichnost beskonechno-zonnykh potentsialov”, Izv. AN SSSR. Ser. matem., 45:2 (1981), 291–320 | MR | Zbl

[2] Novikov S. P., “Periodicheskaya zadacha Kortevega de Friza. I”, Funkts. analiz, 8:3 (1974), 43–53 | MR

[3] Lax P., “Almost periodic Behaviour of Nonlinear Waves”, Adv. in Math., 16 (1975), 368–379 | DOI | MR | Zbl

[4] Marchenko V. A., Ostrovskii I. V., “Kharakteristika spektra operatora Khilla”, Matem. sb., 97:4 (1975), 540–606 | MR | Zbl

[5] Marchenko V. A., Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR