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On the best polynomial approximation of entire transcendental functions in Banach spaces. II

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Ukrainian Mathematical Journal Aims and scope

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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References

  1. 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).

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  2. A. R. Reddy, “Approximation of an entire function,”J. Approxim. Theory,3, No. 1, 128–137 (1970).

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Authors and Affiliations

  1. Institute of Geotechnical Mechanics, Ukrainian Academy of Sciences, Dnepropetrovsk

    S. B. Vakarchuk

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  1. S. B. Vakarchuk
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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

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