Majorants of remainders of Taylor series of bounded holomorphic functions

• Date: 2014
• Author Affiliations: І. Ю. Меремеля — Інститут математики НАН України; В. В. Савчук — Інститут математики НАН України
• Keywords: keywords
• Main Authors: Meremelya, I. Yu., Savchuk, V. V., Меремеля, І. Ю., Савчук, В. В.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2014
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/75
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

We study the behavior on the interval $[0,1]$ of the majorant $R_n$ of the $n$-remainders of Taylor's series for bounded holomorphic functions in the unit disk $\mathbb D$. An extremal problem of finding the $\max|f(z_1)-f(z_2)|,$ $z_1, z_2\in\mathbb D,$ for functions from such class is sol...