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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fourier analysis on the sphere


Author: Thomas O. Sherman
Journal: Trans. Amer. Math. Soc. 209 (1975), 1-31
MSC: Primary 43A85
MathSciNet review: 0390663
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Abstract: A new approach to harmonic analysis on the unit sphere in $ {{\mathbf{R}}^{d + 1}}$ is given, closer in form to Fourier analysis on $ {{\mathbf{R}}^d}$ than the usual development in orthonormal polynomials. Singular integrals occur in the transform formulae. The results generalize to symmetric space.


References [Enhancements On Off] (What's this?)

  • [1] A. Erdelyi et al., Higher transcendental functions. Vol. 2, McGraw-Hill, New York, 1953. MR 15, 419.
  • [2] Sigurđur Helgason, A duality for symmetric spaces with applications to group representations, Advances in Math. 5 (1970), 1–154 (1970). MR 0263988
  • [3] Claus Müller, Spherical harmonics, Lecture Notes in Mathematics, vol. 17, Springer-Verlag, Berlin-New York, 1966. MR 0199449
  • [4] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0390663-1
Keywords: Harmonic analysis, Fourier transform, sphere, symmetric space, ultraspherical polynomials, singular integral
Article copyright: © Copyright 1975 American Mathematical Society