Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

Klotz, Lutz, and Zagorodnyuk, Sergey M.. "Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space." Serdica Mathematical Journal 35.2 (2009): 147-168. <http://eudml.org/doc/281524>.

@article{Klotz2009,
abstract = {2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.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.},
author = {Klotz, Lutz, Zagorodnyuk, Sergey M.},
journal = {Serdica Mathematical Journal},
keywords = {Density of Polynomials; Moment Problem; Measure; density of polynomials; moment problem; measure},
language = {eng},
number = {2},
pages = {147-168},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space},
url = {http://eudml.org/doc/281524},
volume = {35},
year = {2009},
}

TY - JOUR
AU - Klotz, Lutz
AU - Zagorodnyuk, Sergey M.
TI - Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space
JO - Serdica Mathematical Journal
PY - 2009
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 2
SP - 147
EP - 168
AB - 2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.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.
LA - eng
KW - Density of Polynomials; Moment Problem; Measure; density of polynomials; moment problem; measure
UR - http://eudml.org/doc/281524
ER -