Abstract
Known approximation theorems of Weierstrass and Lavrent'ev are extended by determining allowable bounds on the values of the coefficients of the approximating polynomials.
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James D. Stafney, “A permissible restriction on the coefficients in uniform polynomial approximation to C[0, 1],” Duke Math. J.,34, No. 3, 393–396 (1967).
M. A. Lavrent'ev, “Sur les fonctions d'une variable complex repre'sentables par des séries des poly-nomes,” Paris (1936).
S. Ya. Khavinson, “Some problems of the completeness of systems,” Dokl. Akad. Nauk SSSR,137, No. 4, 793–796 (1961).
J. Wermer, “Banach algebras and analytic functions,” in Advances in Math.,1, No. 1, 51–102 (1961).
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Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 619–625, November, 1969.
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Khavinson, S.Y. Permissible values of coefficients of polynomials in uniform approximation of continuous functions. Mathematical Notes of the Academy of Sciences of the USSR 6, 834–838 (1969). https://doi.org/10.1007/BF01101413
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DOI: https://doi.org/10.1007/BF01101413