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Literature Cited
N. I. Akhiezer and I. N. Glazman, Theory of Linear Operators in Hilbert Space, Ungar Press.
M. G. Krein and A. A. Nudel'man, The Markov Moment Problem and Extremal Problems [in Russian], Nauka, Moscow (1973).
I. S. Kats and M. G. Krein, “ℛ-functions are analytic functions that map the upper half plane into itself,” Editor's Appendix in: F. Atkinson, Discrete and Continuous Boundary-Value Problems [Russian translation], Mir, Moscow (1968).
N. I. Akhiezer and M. G. Krein, On Certain Questions of Theory of Moments [in Russian], Gosudarstvennoe Ob"edinennoe Nauchno-Tekhnicheskoe Izd., Kharkov (1939).
S. T. Aleksandrov and V. V. Sobolev, “The Loewner-Kurfarev equation for half plane and variation of univalent ℛ-functions,” in: Differential Equations and Their Applications [in Russian], Trudy Tyumen. Gos. Univ. (1980), pp. 8–30.
T. N. Sellyakhova and V. V. Sobolev, “Investigation of the extremal properties of a certain class of univalent conformal mappings of a half plane into itself,” in: Certain Questions of the Modern Theory of Functions [in Russian], Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1976), pp. 142–145.
V. G. Moskvin, T. N. Sellyakhova, and V. V. Sobolev, “Extremal properties of certain classes of functions with fixed first coefficients that map conformally a half plane into itself,” Sib. Mat. Zh.,21, No. 2, 137–154 (1980).
V. Ya. Gutlyanskii, “Parametric representations of univalent functions,” Dokl. Akad. Nauk SSSR,194, No. 4, 750–753 (1970).
V. Ya. Gutlyanskii, “Parametric representations and extremal problems in the theory of univalent functions,” Author's Abstract of Doctoral Dissertation, Physicomathematical Sciences, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1972).
V. I. Popov, “On a variational formula for univalent functions,” in: Questions of Geometric Theory of Functions [in Russian], Tr. Tom. Univ., Vol. 200, No. 5 (1968), pp. 181–183.
V. I. Popov, “L. S. Pontryagin's maximum principle in the theory of univalent functions,” Dokl. Akad. Nauk SSSR,188, No. 3, 532–534 (1969).
S. T. Aleksandrov, “Domains of values of certain systems of functionals in the classes of the functions that are univalent in a half plane,” in: Differential Equations and Their Applications [in Russian], Tr. Tyumen. Gos. Univ. (1980), pp. 31–48.
N. A. Lebedev and I. A. Aleksandrov, “On the method of variations in the classes of the functions that can be represented by means of the Stieltjes integrals,” Trudy Inst. Mat. im. V. A. Steklova Akad. Nauk SSSR,94, 79–89 (1968).
I. A. Aleksandrov, Parametric Continuation in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1976).
I. A. Aleksandrov, S. T. Aleksandrov, and V. V. Sobolev, “Extremal properties of mappings of a half plane into itself,” in: J. Lawrynowicz and J. Siciak (eds.), Complex Analysis, PWN, Warsaw (1983), pp. 7–32.
V. V. Sobolev, “Investigation of extremal problems for classes of the functions that are univalent in a half plane,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Tomsk State Univ. (1969).
V. G. Boltyanskii, Mathematical Methods of Optimal Control [in Russian], Nauka, Moscow (1969).
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Rostov-on-Don. Tyumen. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 27, No. 2, pp. 3–13, March–April, 1986.
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Aleksandrov, S.T., Sobolev, V.V. Extremal problems in certain classes of univalent functions in a half plane that have finite angular residues at infinity. Sib Math J 27, 145–154 (1986). https://doi.org/10.1007/BF00969379
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DOI: https://doi.org/10.1007/BF00969379