2017
Том 69
№ 7

All Issues

On the best polynomial approximation of entire transcendental functions of generalized order

Vakarchuk S. B., Zhir S. I.

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Abstract

We prove a Hadamard-type theorem which connects the generalized order of growth $\rho^*_f(\alpha, \beta)$ of entire transcendental function $f$ with coefficients of its expansion into the Faber series. The theorem is an original extension of a certain result by S. K. Balashov to the case of finite simply connected domain $G$ with the boundary $\gamma$ belonging to the S. Ya. Al'per class $\Lambda^*.$ This enables us to obtain boundary equalities that connect $\rho^*_f(\alpha, \beta)$ with the sequence of the best polynomial approximations of $f$ in some Banach spaces of functions analytic in $G$.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 8, pp 1183-1199.

Citation Example: Vakarchuk S. B., Zhir S. I. On the best polynomial approximation of entire transcendental functions of generalized order // Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1011–1026.

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