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Literature cited
J. L. Walsh, “A closed set of normal orthogonal functions,” Am. J. Math.,45, 5–24 (1923).
R. E. A. C. Paley, “A remarkable system of orthogonal functions,” Proc. London Math. Soc.,34, 241–279 (1932).
N. Ya. Vilenkin, “A class of complete orthogonal systems,” Izv. Akad. Nauk SSSR, Ser. Mat.2, 363–400 (1947).
S. B. Stechkin, “On the approximation of periodic functions by the Fejer sums,” Trudy MI AN SSSR,62, 48–60 (1961).
V. E. Geit, “Exactness of some inequalities in the approximation theory,” Mat. Zametki,10, No. 5, 571–582 (1971).
K. I. Oskolkov, “On the Lebesgue inequality in the uniform metric and on a set of full measure,” Mat. Zametki,18, No. 4, 515–526 (1975).
S. B. Stechkin, “On the approximation of periodic functions by de la Vallee Poussin sums,” Analysis Mathematica,4, 61–74 (1978).
V. Damen, “On the best approximation and de la Vallee Poussin sums,” Mat. Zametki,23, No. 5, 671–683 (1978).
K. I. Oskolov, “On the Lebesgue inequality in mean,” Mat. Zametki,25, No. 4, 551–555 (1979).
S. P. Baiborodov, “Function approximation by de la Vallee Poussin sums,” Mat. Zametki,27, No. 1, 33–48 (1980).
S. P. Baiborodov, “An approximation of multivariable functions by the orthogonal de la Vallee Poussin sums,” Mat. Zametki,29, No. 5, 711–730 (1981).
Wang Kunyang, “The estimation of the multiple de la Vallee Poussin square remainder,” Chinese Ann. Math.,3, No. 6, 789–802 (1982).
S. P. Baiborodov, “The Lebesgue constants and the function approximation by the orthogonal Fourier sums in LP(Tm),” Mat. Zametki,34, No. 1, 77–90 (1983).
S. P. Baiborodov, “The approximation of functions of many variables by the Fejer sums,” Mat. Zametki,36, No. 1, 123–136 (1984).
N. A. Il'yasov, “The approximation of periodic functions by the Zygmund conjugates,” Mat. Zametki,39, No. 3, 367–382 (1986).
I. I. Sharapudinov, “On the best approximation and the Fourier-Jacobi sums,” Mat. Zametki,34, No. 5, 651–661 (1983).
B. S. Kashin and A. A. Saakyan, Orthogonal Series [in Russian], Nauka, Moscow (1984).
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Translated from Matematicheskie Zametki, Vol. 41, No. 1, pp. 23–33, January, 1987.
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Baiborodov, S.P. Approximation of functions by the Fourier-Walsh sums. Mathematical Notes of the Academy of Sciences of the USSR 41, 15–22 (1987). https://doi.org/10.1007/BF01159523
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DOI: https://doi.org/10.1007/BF01159523