2019
Том 71
№ 11

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

Bakan A. G.

Abstract

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 the spaces $C_w^0$.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 5, pp 750–762.

Citation Example: Bakan A. G. Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ // Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 610-622.

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