대한수학회지 (Journal of the Korean Mathematical Society)

  • 제41권4호
  • /
  • Pages.755-772
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  • 2004
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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FOURIER INVERSION OF DISTRIBUTIONS ON THE SPHERE

  • 발행 : 2004.07.01
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초록

We show that the Fourier-Laplace series of a distribution on the sphere is uniformly Cesaro-summable to zero on a neighborhood of a point if and only if this point does not belong to the support of the distribution. Similar results on the ball and on the real projective space are also proved.

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참고문헌

  1. Ann. Global Anal. Geom. v.18 Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type W. O. Bray;M. A. Pinsky https://doi.org/10.1023/A:1006712230719
  2. Geometric Applications of Fourier Series and Spherical Harmonics H. Groemer
  3. Divergent Series G. H. Hardy
  4. Ensembles parfaits et series trigonometriques J.-P. Kahane;R. Salem
  5. Distributions, analyse de Fourier, operateurs aux derivees partielles v.1 Vo Khac Khoan
  6. J. Math. Pures Appl. v.3 Recherches sur la sommabilite des series ultraspheriques par la methode des moyennes arithmetiques E. Kogbetliantz
  7. Introduction to Fourier Analysis on Euclidean Spaces E. M. Stein;G. Weiss
  8. Collected Papers v.2 Asymptotische Entwicklung der Jacobischen Polynome G. Szego;R. Askey(ed.)
  9. Orthogonal polynomials G. Szego
  10. Studia Math. v.26 Pointwise convergence of distribution expansions G. Walter https://doi.org/10.4064/sm-26-2-143-154
  11. Math. Proc. Cambridge Philos. Soc. v.131 Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls Y. Xu

피인용 문헌

  1. Abel means for orthogonal expansions of distributions on spheres, balls and simplices vol.433, pp.1, 2016, https://doi.org/10.1016/j.jmaa.2015.08.006