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

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля
  • S. I. Zhir


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 $G$.

How to Cite
Vakarchuk, S. B., and S. I. Zhir. “On the Best Polynomial Approximation of Entire Transcendental Functions of Generalized Order”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 8, Aug. 2008, pp. 1011–1026, https://umj.imath.kiev.ua/index.php/umj/article/view/3219.
Research articles