The Gaussian measure on algebraic varieties

• Autorzy: Ilka Agricola , Thomas Friedrich
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Gaussian measure; algebraic variety

Kategorie tematyczne

• 58A07: Real-analytic and Nash manifolds
• 28A75: Length, area, volume, other geometric measure theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 159
• Numer: 1
• Strony: 91-98

Daty

wydano

1999

otrzymano

1998-04-25

poprawiono

1998-09-08

Twórcy

autor

Ilka Agricola

• Institut für Reine Mathematik, Humboldt-Universität zu Berlin, Ziegelstr. 13 A D-10099 Berlin, Germany

autor

Thomas Friedrich

• Institut für Reine Mathematik, Humboldt-Universität zu Berlin, Ziegelstr. 13 A D-10099 Berlin, Germany

Bibliografia

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• [Mi1] J. Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964), 275-280.
• [Mi2] J. Milnor, Euler characteristics and finitely additive Steiner measures, in: Collected Papers, Vol. 1, Publish or Perish, 1994, 213-234.
• [Rud] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1966.
• [Sto1] W. Stoll, The growth of the area of a transcendental analytic set. I, Math. Ann. 156 (1964), 47-78.
• [Sto2] W. Stoll, The growth of the area of a transcendental analytic set. II, ibid. 156 (1964), 144-170.