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References
S. P. Diliberto and E. G. Straus, “On the approximation of a function of several variables by the sum of functions of fewer variables,” Pacific J. Math.,1, No. 1, 195–210 (1951).
Yu. P. Ofman, “On best approximation of functions in two variables by the functions of the formϕ(x) + Ψ(y),” Izv. Akad. Nauk SSSR Ser. Mat.,25, No. 2, 239–252 (1961).
V. P. Motornyi, “On the question of best approximation of functions in two variables by the functions of the formϕ(x) +Ψ(y),” Izv. Akad. Nauk SSSR Ser. Mat.,27, No. 6, 1211–1214 (1963).
V. P. Motornyi, “On the question of best approximation of functions in two variables by the functions of the formϕ(x) + Ψ(y),” in: Studies on Contemporary Problems of the Constructive Theory of Functions [in Russian], Baku, 1965, pp. 66–72.
S. Ya. Khavinson, “A Chebyshëv-type theorem for approximation of functions in two variables by the sumsϕ(x) + Ψ(y),” Izv. Akad. Nauk SSSR Ser. Mat.,33, No. 4, 650–666 (1969).
R. C. Buck, “On approximation theory and functional equations,” J. Approx. Theory,5, No. 3, 228–237 (1972).
D. E. Marshall and A. G. O'Farrell, “Approximation by a sum of two algebras. The lightning bolt principle,” J. Functional Anal.,52, No. 3, 353–366 (1983).
S. Ya. Khavinson, “On the representation and approximation of functions in two variables by linear superpositions,” in: Questions in Mathematics, Continuum Mechanics, and Applications to Mathematical Methods in Civil Engineering [in Russian], Moscow, 1987, pp. 89–92.
M. M. Day, Normed Linear Spaces [Russian translation], Izdat. Inostr. Lit., Moscow (1961).
V. I. Arnol'd, “On functions of three variables,” Dokl. Akad. Nauk SSSR,114, No. 4, 679–681 (1957).
D. E. Marshall and A. G. O'Farrell, “Uniform approximation by real functions,” Fund. Math.,104, 203–211 (1979).
V. Z. Vulikh, A Short Course in the Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1965).
I. P. Natanson, Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1974).
V. A. Medvedev, “On the sum of two closed algebras of continuous functions on a compactum,” Funktsional. Anal. i Prilozhen.,27, No. 1, 33–36 (1993).
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The research was supported by the State Committee for Higher Education of the Russian Federation (Grant 2-16-4-24) and the International Science Foundation (Grant MB 6000).
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 819–827, July–August, 1995.
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Garkavi, A.L., Medvedev, V.A. & Havinson, S.Y. On existence of a best uniform approximation of a function in two variables by the sums ϕ(x) + Ψ(y). Sib Math J 36, 707–713 (1995). https://doi.org/10.1007/BF02107327
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DOI: https://doi.org/10.1007/BF02107327