On some new criteria for infinite differentiability of periodic functions

• Date: 2007
• Main Authors: Serdyuk, A. S., Stepanets, O. I., Shydlich, A. L., Сердюк, А. С., Степанець, О. І., Шидліч, А. Л.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3398
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The set $\mathcal{D}^{\infty}$ of infinitely differentiable periodic functions is studied in terms of generalized $\overline{\psi}$-derivatives defined by a pair $\overline{\psi} = (\psi_1, \psi_2)$ of sequences $\psi_1$ and $\psi_2$ . It is shown that every function $f$ from the set $\mathcal{D}^...