# The Gaussian measure on algebraic varieties

Ilka Agricola; Thomas Friedrich

Fundamenta Mathematicae (1999)

- Volume: 159, Issue: 1, page 91-98
- ISSN: 0016-2736

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topAgricola, Ilka, and Friedrich, Thomas. "The Gaussian measure on algebraic varieties." Fundamenta Mathematicae 159.1 (1999): 91-98. <http://eudml.org/doc/212322>.

@article{Agricola1999,

abstract = {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.},

author = {Agricola, Ilka, Friedrich, Thomas},

journal = {Fundamenta Mathematicae},

keywords = {Gaussian measure; algebraic variety; ring of polynomials; real algebraic variety; Hilbert space},

language = {eng},

number = {1},

pages = {91-98},

title = {The Gaussian measure on algebraic varieties},

url = {http://eudml.org/doc/212322},

volume = {159},

year = {1999},

}

TY - JOUR

AU - Agricola, Ilka

AU - Friedrich, Thomas

TI - The Gaussian measure on algebraic varieties

JO - Fundamenta Mathematicae

PY - 1999

VL - 159

IS - 1

SP - 91

EP - 98

AB - 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.

LA - eng

KW - Gaussian measure; algebraic variety; ring of polynomials; real algebraic variety; Hilbert space

UR - http://eudml.org/doc/212322

ER -

## References

top- [Agr] I. Agricola, Dissertation am Institut für Reine Mathematik der Humboldt-Universität zu Berlin, in preparation.
- [Brö] L. Bröcker, Semialgebraische Geometrie, Jahresber. Deutsch. Math.-Verein. 97 (1995), 130-156.
- [Mau] K. Maurin, Analysis, Vol. 2, Reidel and PWN-Polish Sci. Publ., Dordrecht and Warszawa, 1980.
- [Mi1] J. Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964), 275-280. Zbl0123.38302
- [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. Zbl0126.09502
- [Sto2] W. Stoll, The growth of the area of a transcendental analytic set. II, ibid. 156 (1964), 144-170.

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