Density questions in the classical theory of moments

Berg, Christian, and Christensen, J. P. Reus. "Density questions in the classical theory of moments." Annales de l'institut Fourier 31.3 (1981): 99-114. <http://eudml.org/doc/74510>.

@article{Berg1981,
abstract = {Let $\mu $ be a positive Radon measure on the real line having moments of all orders. We prove that the set $P$ of polynomials is note dense in $L^p(\{\bf R\},\mu )$ for any $p&gt;2$, if $\mu $ is indeterminate. If $\mu $ is determinate, then $P$ is dense in $L^p(\{\bf R\},\mu )$ for $1\le p \le 2$, but not necessarily for $p&gt;2$. The compact convex set of positive Radon measures with same moments as $\mu $ is studied in some details.},
author = {Berg, Christian, Christensen, J. P. Reus},
journal = {Annales de l'institut Fourier},
keywords = {density questions; classical theory of moments; positive Radon measure},
language = {eng},
number = {3},
pages = {99-114},
publisher = {Association des Annales de l'Institut Fourier},
title = {Density questions in the classical theory of moments},
url = {http://eudml.org/doc/74510},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Berg, Christian
AU - Christensen, J. P. Reus
TI - Density questions in the classical theory of moments
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 3
SP - 99
EP - 114
AB - Let $\mu $ be a positive Radon measure on the real line having moments of all orders. We prove that the set $P$ of polynomials is note dense in $L^p({\bf R},\mu )$ for any $p&gt;2$, if $\mu $ is indeterminate. If $\mu $ is determinate, then $P$ is dense in $L^p({\bf R},\mu )$ for $1\le p \le 2$, but not necessarily for $p&gt;2$. The compact convex set of positive Radon measures with same moments as $\mu $ is studied in some details.
LA - eng
KW - density questions; classical theory of moments; positive Radon measure
UR - http://eudml.org/doc/74510
ER -