The Gaussian measure on algebraic varieties
Volume 159 / 1999
Fundamenta Mathematicae 159 (1999), 91-98
DOI: 10.4064/fm-159-1-91-98
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.
