Abstract
Necessary and sufficient conditions for best approximations of functions in the\(L_{(1 - X^2 )^\alpha }^2 \) (−1,1) metric, −1/2≤α<1/2 to zero at a certain rate are established (for α=−1/2 known results are obtained). Inequalities for algebraic polynomials are used in the reasoning.
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Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 587–596, May, 1968.
I wish to thank my research director G. I. Natanson for his valuable advices.
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Rafal'son, S.Z. Mean approximation of functions by Fourier-Gegenbauer sums. Mathematical Notes of the Academy of Sciences of the USSR 3, 374–379 (1968). https://doi.org/10.1007/BF01150992
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DOI: https://doi.org/10.1007/BF01150992