Literature Cited
M. Schiffer and D. C. Spencer, Functionals of Finite Riemann Surfaces, Princeton Univ. Press (1954).
N. I. Zhukova and E. I. Zverovich, The Riemann Surfaces of Regular 2n-gons [in Russian], Moscow (1976); Deposited in the All-Union Institute of Scientific and Technical Information on March 22, 1976 at No. 887-76.
G. Springer, Introduction to Riemann Surfaces, Addison-Wesley, Reading (Mass.) (1957).
F. D. Gakhov, Boundary Value Problems, Pergamon (1972).
G. P. Cherepanov, “Solution of a linear boundary-value problem for two functions and its application to certain mixed-value problems of theory of elasticity,” Prikl. Mat. Mekh.,26, No. 5, 907–912 (1962).
G. P. Cherepanov, “On an integrable case of the Riemann boundary-value problem for several functions,” Dokl. Akad. Nauk SSSR,161, No. 6, 1285–1288 (1965).
E. I. Zverovich, “Boundary-value problems of the theory of analytic functions in Holder classes on Riemann surfaces,” Usp. Mat. Nauk,26, No. 1, 113–179 (1971).
E. I. Zverovich, “The mixed-value problem of theory of elasticity for the plane with cuts that lie on the real axis,” in: Proceedings of Symposium on Mechanics of Continuous Medium and Related Problems of Analysis [in Russian], Vol. 1, Metsniereba, Tbilisi (1973), pp. 103–114.
E. I. Zverovich, “On the construction of the field of algebraic functions that corresponds to a given covering of the sphere,” Dokl. Akad. Nauk BSSR,29, No. 2, 104–107 (1985).
N. G. Chebotarev, Theory of Algebraic Functions [in Russian], Gostekhizdat, Moscow-Leningrad (1948).
O. Forster, Riemann Surfaces [Russian translation], Mir, Moscow (1980).
J. Plemelj, “Riemannsche Funktionenscharen mit gegebener Monodromiegruppe,” Monatsh. Math. Phys.-Jahrgang,19, 211–245 (1908).
E. I. Zverovich and L. I. Pomerantseva, “The Riemann problem for n pairs of functions with permutation type matrices,” Dokl. Akad. Nauk SSSR,217, No. 1, 20–23 (1974).
L. I. Pomerantseva, “An algebraic method for the determination of the equation of a given Riemann surface,” Mat. Issled., Kishinev,9, No. 3(33), 201–205 (1974).
V. E. Kruglov, “Partial indexes, abelian differentials of first kind, and the equation of a surface, given by a finite abelian permutation group,” Sib. Mat. Zh.,12, No. 6, 87–101 (1981).
V. E. Kruglov, “On the structure of partial indexes of the Riemann problem with permutation type matrices,” Mat. Zametki,35, No. 2, 169–176 (1984).
B. V. Shabat, Introduction to Complex Analysis [in Russian], Part 1, Nauka, Moscow (1985).
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).
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Minsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 6, pp. 32–43, November–December, 1987.
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Zverovich, É.I. An algebraic method for the construction of the basic functionals of a Riemann surface, given in the form of a finite-sheeted covering of the sphere. Sib Math J 28, 889–898 (1987). https://doi.org/10.1007/BF00969466
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DOI: https://doi.org/10.1007/BF00969466