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Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space C w 0

Authors:	Bakan A G

Institution:	(1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

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 .

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