Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$

• Date: 2002
• Main Authors: Bakan, A. G., Бакан, А. Г.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4099
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For an arbitrary function $w:\mathbb{R} \to \left[ {0,1} \right]$, we determine the general form of a linear continuous functional on the space $C_w^0$. The criterion for denseness of polynomials in the space $L_2 \left( {\mathbb{R},d\mu } \right)$ established by Hamburger in 1921 is extended to...