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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Fourier analysis on the sphere
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by Thomas O. Sherman PDF
Trans. Amer. Math. Soc. 209 (1975), 1-31 Request permission

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
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  • 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, DOI 10.1017/CBO9780511608759
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 1-31
  • MSC: Primary 43A85
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0390663-1
  • MathSciNet review: 0390663