On the Best Approximation in the Mean by Algebraic Polynomials with Weight and the Exact Values of Widths for the Classes of Functions

• Date: 2013
• Main Authors: Vakarchuk, S. B., Shvachko, A. V., Вакарчук, С. Б., Швачко, А. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2540
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The exact value of the extremal characteristic is obtained on the class L 2 r (D ρ ), where r ∈ ℤ+; \( {D}_{\rho} = \sigma (x)\frac{d^2}{d{ x}^2}+\tau (x)\frac{d}{d x} \) , σ and τ are polynomials of at most the second and first degrees, respectively, ρ is a weight function, 0 < p...