We present a brief survey of the development of functional analysis in Ukraine and the problems of infinite-dimensional analysis posed and solved for thousands of years, which laid the foundations of this branch of mathematics.
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References
S. Banach, A Course in Functional Analysis [in Ukrainian], Radyans’ka Shkola, Kyiv (1948).
Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
N. Bourbaki, Eléments d’Historie des Mathématiques, Hermann, Paris (1960).
M. L. Horbachuk and A. M. Samoilenko, “Mykhailo Vasyl’ovych Ostrohrads’kyi and his role in the development of mathematics,” Ukr. Mat. Zh., 53, No. 8, 1011–1023 (2001); English translation: Ukr. Math. J., 53, No. 8, 1207–1219 (2001).
M. L. Gorbachuk and V. I. Gorbachuk, M. G. Krein’s Lectures on Entire Operators, Birkhäuser, Basel (1997).
M. L. Horbachuk, “Heorhii Feodosiiovych Voronyi,” in: Prominent Figures of Ukraine [in Ukrainian], MAUP, Kyiv (2004), pp. 186–190.
O. M. Bogolyubov, Yu. O. Mytropol’skyi, A. M. Samoilenko, and M. L. Horbachuk, “Mathematics,” in: History of Ukrainian Culture [in Ukrainian], Vol. 5, Book 3, Naukova Dumka, Kyiv (2012), pp. 449–480.
L. Euler, Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Latissimo Sensu Accepti, Lausannæ & Genevæ (1744).
I. Kepler, Nova Stereometria Doliorum Vinariorum, Linz (1615).
F. Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Vol. 1, Springer, Berlin (1926).
M. G. Krein, “Analytic problems and results in the theory of operators in Hilbert spaces,” in: Proc. of the Internat. Congr. of Mathematicians, Mir, Moscow (1968), pp. 189–216.
J. L. Lagrange, Méchanique Analytique, Vols. 1, 2, Veuve Courcier, Paris (1811–1815).
S. Ya. Lur’e, Archimedes [in Russian], Izd. Akad. Nauk SSSR, Moscow (1945).
A. Yu. Luchka and T. F. Luchka, Appearance and Development of the Direct Methods of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1985).
S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).
M. V. Ostrogradskii, Complete Collection of Works [in Russian], Vols. 1, 3, Akad. Nauk SSSR, Moscow (1959–1961).
A. B. Paplauskas, Trigonometric Series from Euler to Lebesgue [in Russian], Nauka, Moscow (1966).
B. Riemann, Works [Russian translation], Gostekhizdat, Moscow (1948).
C. Reid, Hilbert., Springer, Berlin (1970).
K. A. Rybnikov, History of Mathematics [in Russian], Moscow University, Moscow (1974).
V. S. Ryzhii and I. G. Nikolaenko, History of Mathematics [in Russian], Kharkov University, Kharkov (2013).
V. A. Sologub, Development of the Theory of Elliptic Equations in the 18th and 19th Centuries [in Russian], Naukova Dumka, Kiev (1975).
S. P. Timoshenko, History of the Science of Strength of Materials [in Russian], Gostekhizdat, Moscow (1957).
V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1979).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 8, pp. 1058–1073, August, 2014.
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Horbachuk, M.L. History of the Appearance of Infinite-Dimensional Analysis and its Development in Ukraine. Ukr Math J 66, 1185–1199 (2015). https://doi.org/10.1007/s11253-015-1002-7
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DOI: https://doi.org/10.1007/s11253-015-1002-7