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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
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
S.
Bochner, Positive zonal functions on spheres, Proc. Nat. Acad.
Sci. U. S. A. 40 (1954), 1141–1147. MR 0068127
(16,834e)
- [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
(11,498b)
- [6]
Sigurđur
Helgason, Differential geometry and symmetric spaces, Pure and
Applied Mathematics, Vol. XII, Academic Press, New York, 1962. MR 0145455
(26 #2986)
- [7]
Henry
Helson, Isomorphisms of abelian group algebras, Ark. Mat.
2 (1953), 475–487. MR 0058138
(15,327g)
- [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, http://dx.doi.org/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
(27 #2808)
- [11]
Walter
Rudin, Projections on invariant
subspaces, Proc. Amer. Math. Soc. 13 (1962), 429–432. MR 0138012
(25 #1460), http://dx.doi.org/10.1090/S0002-9939-1962-0138012-4
- [1]
- S. Bochner, Positive zonal functions on spheres, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1141-1147. MR 0068127 (16:834e)
- [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 on symmetric spaces, Dokl. Akad. Nauk. SSSR 70 (1950), 5-8. MR 0033832 (11:498b)
- [6]
- S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
- [7]
- H. Helson, Isomorphisms of abelian group algebras, Ark. Mat. 2 (1953), 475-487. MR 0058138 (15:327g)
- [8]
- I. I. Hirschman, Jr., Harmonic analysis and ultraspherical polynomials, Proceedings of the Conference on Harmonic Analysis, Cornell, 1956.
- [9]
- L. Koschmieder, Über die
-Summierbarkeit gewisser Reihen von Didon und Appell, Math. Ann. 104 (1931), 387-402. MR 1512676
- [10]
- W. Rudin, Fourier analysis on groups, Interscience, New York, 1962. MR 0152834 (27:2808)
- [11]
- -, Projections in invariant subspaces, Proc. Amer. Math. Soc. 13 (1962), 429-432. MR 0138012 (25:1460)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1966-0203371-9
PII:
S 0002-9947(1966)0203371-9
Article copyright:
© Copyright 1966 American Mathematical Society
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