Fourier inversion of distributions on projective spaces

Francisco Javier González Vieli

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 437-441
  • ISSN: 0010-2628

Abstract

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We show that the Fourier-Laplace series of a distribution on the real, complex or quarternionic projective space is uniformly Cesàro-summable to zero on a neighbourhood of a point if and only if this point does not belong to the support of the distribution.

How to cite

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Vieli, Francisco Javier González. "Fourier inversion of distributions on projective spaces." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 437-441. <http://eudml.org/doc/249861>.

@article{Vieli2006,
abstract = {We show that the Fourier-Laplace series of a distribution on the real, complex or quarternionic projective space is uniformly Cesàro-summable to zero on a neighbourhood of a point if and only if this point does not belong to the support of the distribution.},
author = {Vieli, Francisco Javier González},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {distribution; projective space; Fourier-Laplace series; Cesàro summability; Fourier-Laplace series; Cesàro summability},
language = {eng},
number = {3},
pages = {437-441},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fourier inversion of distributions on projective spaces},
url = {http://eudml.org/doc/249861},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Vieli, Francisco Javier González
TI - Fourier inversion of distributions on projective spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 437
EP - 441
AB - We show that the Fourier-Laplace series of a distribution on the real, complex or quarternionic projective space is uniformly Cesàro-summable to zero on a neighbourhood of a point if and only if this point does not belong to the support of the distribution.
LA - eng
KW - distribution; projective space; Fourier-Laplace series; Cesàro summability; Fourier-Laplace series; Cesàro summability
UR - http://eudml.org/doc/249861
ER -

References

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  1. Fomenko A.T., Symplectic Geometry, Gordon and Breach Science Publishers, New York, 1988. Zbl0873.58031MR0994805
  2. González Vieli F.J., Fourier inversion of distributions on the sphere, J. Korean Math. Soc. 41 (2004), 755-772. (2004) Zbl1066.46031MR2068151
  3. Hardy G.H., Divergent Series, Clarendon Press, Oxford, 1949. Zbl0897.01044MR0030620
  4. Helgason S., Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. Zbl0122.39901MR0145455
  5. Kahane J.-P., Salem R., Ensembles parfaits et séries trigonométriques, Hermann, Paris, 1963. Zbl0856.42001MR0160065
  6. Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971. Zbl0232.42007MR0304972
  7. Walter G., Pointwise convergence of distribution expansions, Studia Math. 26 (1966), 143-154. (1966) Zbl0144.37401MR0190624

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