The Gaussian measure on algebraic varieties

Agricola, Ilka; Friedrich, Thomas

Fundamenta Mathematicae, Tome 159 (1999), p. 91-98 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety $M \subset ℝ^{n}$ is dense in the Hilbert space $L^{2} (M, e^{- {| x |}^{2}} d μ)$ , where dμ denotes the volume form of M and $d ν = e^{- {| x |}^{2}} d μ$ the Gaussian measure on M.

Publié le : 1999-01-01

Zbl 0924.58005

EUDML-ID : urn:eudml:doc:212322

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     author = {Ilka Agricola and Thomas Friedrich},
     title = {The Gaussian measure on algebraic varieties},
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     year = {1999},
     pages = {91-98},
     zbl = {0924.58005},
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Agricola, Ilka; Friedrich, Thomas. The Gaussian measure on algebraic varieties. Fundamenta Mathematicae, Tome 159 (1999) pp. 91-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv159i1p91bwm/

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