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Title: Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space
Authors: Klotz, Lutz
Zagorodnyuk, Sergey M.
Keywords: Density of Polynomials
Moment Problem
Issue Date: 2009
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 2, (2009), 147p-168p
Abstract: In this paper we consider an L^2 type space of scalar functions L^2 M, A (R u iR) which can be, in particular, the usual L^2 space of scalar functions on R u iR. 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 R with respect to a non-negative Hermitian matrix measure. The completness of L^2 M, A (R u iR ) is also established.
Description: 2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.
ISSN: 1310-6600
Appears in Collections:Volume 35, Number 2

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