Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions

• Date: 2004
• Main Authors: Pleshakov, M. G., Popov, P. A., Плешаков, М. Г., Попов, П. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3734
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider a 2π-periodic function f continuous on \(\mathbb{R}\) and changing its sign at 2s points y i ∈ [−π, π). For this function, we prove the existence of a trigonometric polynomial T n of degree ≤n that changes its sign at the same points y i and is such that the deviation | f(x) − T n(x...