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 0w . 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 0w .
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Bakan, A.G. Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space C 0w . Ukrainian Mathematical Journal 54, 750–762 (2002). https://doi.org/10.1023/A:1021627228761
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DOI: https://doi.org/10.1023/A:1021627228761