The Gaussian Measure On Algebraic Varieties

1998/04/24 by Ilka Agricola, Thomas Friedrich, Agricola, Ilka +1
Economics, Econometrics and Finance · Mathematics · #14P05 #28A25 #46E99 #58A99 #Differential Geometry (math.DG) #FOS: Mathematics #Stochastic processes and financial applications #math.DG #msc:14P05 #msc:28A25 #msc:46E99 #msc:58A99

paper · pdf · doi:10.48550/arxiv.math/9804116

Latex2.09, 6 pages

arxiv created 1998/04/24 · openalex publication_date 1998/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the ring \Aff\RM of all polynomials defined on a real algebraic variety M⊂\Rⁿ is dense in the Hilbert space L²(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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