On uniform approximations of almost periodic functions by entire functions of finite degree

• Date: 1995
• Main Authors: Timan, M. F., Тиман, М. Ф.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5528
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We give a new proof of the well-known Bernshtein statement that, among entire functions of degree $≤ σ$ which realize the best uniform approximation (of degree $σ$) of a periodic function on $(−∞,∞)$, there is a trigonometric polynomial of degree $≤ σ$. We prove an analog of the mentioned Bernshtein...