Klotz, L.; Zagorodnyuk, S. M. Density of polynomials in the \(L^2\) space on the real and the imaginary axes and in a Sobolev space. (English) Zbl 1224.41018 Serdica Math. J. 35, No. 2, 147-168 (2009). Summary: We consider an \(L^2\) type space of scalar functions \(L^2_{M,A}({\mathbb R}\cup i{\mathbb R})\) which, in particular, can be the usual \(L^2\) space of scalar functions on \({\mathbb R}\cup i{\mathbb R}\). We find conditions for density of polynomials in this space using a connection with the \(L^2\) space of square-integrable matrix-valued functions on \({\mathbb R}\) with respect to a non-negative Hermitian matrix measure. The completeness of \(L^2_{M,A}({\mathbb R}\cup i{\mathbb R})\) is also established. Cited in 1 Document MSC: 41A10 Approximation by polynomials 30E10 Approximation in the complex plane 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Keywords:density of polynomials; moment problem; measure PDFBibTeX XMLCite \textit{L. Klotz} and \textit{S. M. Zagorodnyuk}, Serdica Math. J. 35, No. 2, 147--168 (2009; Zbl 1224.41018)