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

Klotz, Lutz; Zagorodnyuk, Sergey M.

Serdica Mathematical Journal (2009)

- Volume: 35, Issue: 2, page 147-168
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topKlotz, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.