Abstract
We study the behavior of the best approximations\(E_n(f)_{E'}{_p} \) of entire transcendental functionsf(z) of the order ρ=0 by polynomials of at mostn th degree in the metric of the spaceE′ p(Ω),p≥1. In particular, we describe the relationship between the best approximations\(E_n(f)_{E'}{_p} \) and the logarithmic order ρ L and type σ L of the functionf(z).
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S. B. Vakarchuk, “On the best polynomial approximation of entire transcendental functions in Banach spaces. I,”Ukr. Mat. Zh.,46, No. 9, 1123–1133 (1994).
A. R. Reddy, “Approximation of an entire function,”J. Approxim. Theory,3, No. 1, 128–137 (1970).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1318–1322, October, 1994.
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Vakarchuk, S.B. On the best polynomial approximation of entire transcendental functions in Banach spaces. II. Ukr Math J 46, 1451–1456 (1994). https://doi.org/10.1007/BF01066088
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DOI: https://doi.org/10.1007/BF01066088