Integration of the intertwining operator for h-harmonic polynomials associated to reflection groups

Proceedings of the American Mathematical Society

Volumn 125, Issue 10, 1997, Pages 2963-2973

  Yuan, X U ^a  

^a UNIVERSITY OF OREGON   (United States)

Author keywords

H harmonics; Intertwining operator; Orthogonal polynomials in several variables; Reflection groups; Sphere

Indexed keywords

EID: 0040361697     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. R. Askey, Orthogonal polynomials and special functions, SIAM, Philadelphia, 1975. MR 58:1288
2. C. Dunkl, Reflection groups and orthogonal polynomials on the sphere, Math. Z. 197 (1988), 33-60.MR 89b:42016
3. C. Dunkl, Differential-difference operators associated to reflection groups,Trans. Amer. Math. Soc. 311 (1989), 167-183.MR 90k:33027
4. C. Dunkl, Integral kernels with reflection group invariance,Can. J. Math.43 (1991), 12131227.MR 93g:33012
5. C. Dunkl, Intertwining operators associated to the group 83,Trans. Amer. Math. Soc. 347 (1995), 3347-3374. CMP 95:14
6. A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. 2, McGraw-Hill, New York, 1953.MR84h:33001b
7. G. J. Heckman, Hypergeometric and Spherical Functions, Harmonic Analysis and Special Functions on Symmetric Spaces, Academic Press, San Diego, 1994.
8. I.G. Macdonald, Some conjectures for root systems, SIAM. J. Math. Anal. 13 (1982), 9881007.MR 84h:17006a
9. E.M. Opdam, Some applications of hypergeometric shift operators, Invent. Math. 98 (1989), 1-18.MR 91h:33024
10. H. Szegö, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. vol.23, Providence, RI, 1975.
11. Y. Xu, On multivariate orthogonal polynomials, SIAM J. Math. Anal. 24 (1993), 783-794.MR 941:42031
12. Y. Xu, Summability of Fourier orthogonal series for Jacobi weight on a ball in Rd (to appear).
13. Y. Xu, Orthogonal polynomials for a family of product weight functions on the spheres, Canadian J. Math. 49 (1997), 175-192.
14. A. Zygmund, Trigonometric Series, 2th ed., Cambridge Univ. Press, Cambridge, 1968.MR 38:4882