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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?)

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  • Claus Müller, Spherical harmonics, Lecture Notes in Mathematics, vol. 17, Springer-Verlag, Berlin-New York, 1966. MR 0199449
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Keywords: Harmonic analysis, Fourier transform, sphere, symmetric space, ultraspherical polynomials, singular integral
Article copyright: © Copyright 1975 American Mathematical Society