Abstract
We study the behavior of the best approximationsE n (ϕ) p of entire transcendental functions ϕ(z) of the order ρ=∞ by polynomials of at mostn th degree in the metric of the Banach space E′p(Ω) of functions /tf(z) analytic in a bounded simply connected domain Ω with rectifiable Jordan boundary and such that
.
In particular, we describe the relationship between the best approximationsE n (ϕ)p and theq-order andq-type of the function ϕ(z).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1123–1133, September, 1994.
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Vakarchuk, S.B. On the best polynomial approximation of entire transcendental functions in banach spaces. I. Ukr Math J 46, 1235–1247 (1994). https://doi.org/10.1007/BF01059415
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DOI: https://doi.org/10.1007/BF01059415