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The Gaussian Measure On Algebraic Varieties

Ilka Agricola·Thomas Friedrich
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Abstract

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

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Ilka Agricola, Thomas Friedrich. 1998-04-24. The Gaussian Measure On Algebraic Varieties. https://arxiv.org/abs/math/9804116

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