Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 317

The Gaußian Measure on Algebraic Varieties

I. Agricola and T. Friedrich

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

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