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Transactions of the American Mathematical Society

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

 

 

Operators and harmonic analysis on the sphere


Author: Charles F. Dunkl
Journal: Trans. Amer. Math. Soc. 125 (1966), 250-263
MSC: Primary 22.65; Secondary 42.50
MathSciNet review: 0203371
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  • [1] S. Bochner, Positive zonal functions on spheres, Proc. Nat. Acad. Sci. U. S. A. 40 (1954), 1141–1147. MR 0068127
  • [2] E. Cartan, Sur la determination d'un système orthogonal complet dans un espace de Riemann symmetrique clos, Rend. Circ. Mat. Palermo 53 (1929), 217-252.
  • [3] C. F. Dunkl, Harmonic analysis on spheres, Ph.D. Thesis, University of Wisconsin, Madison, 1965.
  • [4] A. Erdélyi, et al., Higher transcendental functions (Bateman Manuscript Project), Vols. I, II, McGraw-Hill, New York, 1953.
  • [5] I. M. Gel′fand, Spherical functions in symmetric Riemann spaces, Doklady Akad. Nauk SSSR (N.S.) 70 (1950), 5–8 (Russian). MR 0033832
  • [6] Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
  • [7] Henry Helson, Isomorphisms of abelian group algebras, Ark. Mat. 2 (1953), 475–487. MR 0058138
  • [8] I. I. Hirschman, Jr., Harmonic analysis and ultraspherical polynomials, Proceedings of the Conference on Harmonic Analysis, Cornell, 1956.
  • [9] Lothar Koschmieder, Über die 𝐶-Summierbarkeit gewisser Reihen von Didon und Appell, Math. Ann. 104 (1931), no. 1, 387–402 (German). MR 1512676, 10.1007/BF01457947
  • [10] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834
  • [11] Walter Rudin, Projections on invariant subspaces, Proc. Amer. Math. Soc. 13 (1962), 429–432. MR 0138012, 10.1090/S0002-9939-1962-0138012-4

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DOI: http://dx.doi.org/10.1090/S0002-9947-1966-0203371-9
Article copyright: © Copyright 1966 American Mathematical Society