The Gaussian measure on algebraic varieties

@article{Agricola1999,
abstract = {We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety $M⊂ℝ^n$ is dense in the Hilbert space $L^2(M,e^\{-|x|^2\}dμ)$, where dμ denotes the volume form of M and $dν = e^\{-|x|^2\}dμ$ the Gaussian measure on M.},
author = {Agricola, Ilka, Friedrich, Thomas},
journal = {Fundamenta Mathematicae},
keywords = {Gaussian measure; algebraic variety; ring of polynomials; real algebraic variety; Hilbert space},
language = {eng},
number = {1},
pages = {91-98},
title = {The Gaussian measure on algebraic varieties},
url = {http://eudml.org/doc/212322},
volume = {159},
year = {1999},
}

TY - JOUR
AU - Agricola, Ilka
AU - Friedrich, Thomas
TI - The Gaussian measure on algebraic varieties
JO - Fundamenta Mathematicae
PY - 1999
VL - 159
IS - 1
SP - 91
EP - 98
AB - We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety $M⊂ℝ^n$ is dense in the Hilbert space $L^2(M,e^{-|x|^2}dμ)$, where dμ denotes the volume form of M and $dν = e^{-|x|^2}dμ$ the Gaussian measure on M.
LA - eng
KW - Gaussian measure; algebraic variety; ring of polynomials; real algebraic variety; Hilbert space
UR - http://eudml.org/doc/212322
ER -