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

• Date: 2008
• Main Authors: Vakarchuk, S. B., Zhir, S. I., Вакарчук, С. Б., Жир, С. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3219
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...