Abstract
We give an estimate of the rapidity of convergence of certain linear means of the orthogonal series Σ ∞k =0 ck ι k (x) to the functionf (x) εL2 (a, b) defined by this series according to the Riesz-Fisher theorem for almost all x ε(a, b). The results obtained are, in a certain sense, final.
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G. Aleksich, Problems of Convergence of Orthogonal Series [in Russian], Moscow (1963).
A. O. Gel'fond, Finite Difference Calculus [in Russian], Moscow (1967).
L. Leindler, “Über Approximation mit Orthogonalreihenmitteln unter strukturellen Bedingungen,” Acta. Sci. Math., 15, 57–62 (1964).
V. A. Andrienko, “On the rapidity of approximation of functions by the (C, 1) means of their orthogonal developments,” Izv. Vysshikh Uchebnykh Zaved., No. 3 (1967), Notes.
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Translated from Matematicheskie Zametki, Vol. 3, No. 3, pp. 345–356, March, 1968.
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Storozhenko, É.A. Approximation by linear methods of summation of orthogonal series. Mathematical Notes of the Academy of Sciences of the USSR 3, 218–224 (1968). https://doi.org/10.1007/BF01387338
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DOI: https://doi.org/10.1007/BF01387338