Integration of the intertwining operator for harmonic polynomials associated to reflection groups
Author:
Yuan Xu
Journal:
Proc. Amer. Math. Soc. 125 (1997), 29632973
MSC (1991):
Primary 33C50, 33C45, 42C10
MathSciNet review:
1402890
Fulltext PDF Free Access
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Abstract: Let be the intertwining operator with respect to the reflection invariant measure on the unit sphere in Dunkl's theory on spherical harmonics associated with reflection groups. Although a closed form of is unknown in general, we prove that where is the unit ball of and is a constant. The result is used to show that the expansion of a continuous function as Fourier series in harmonics with respect to is uniformly Cesáro summable on the sphere if , provided that the intertwining operator is positive.
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Additional Information
Yuan Xu
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 974031222
Email:
yuan@math.uoregon.edu
DOI:
http://dx.doi.org/10.1090/S0002993997039865
PII:
S 00029939(97)039865
Keywords:
Orthogonal polynomials in several variables,
sphere,
$h$harmonics,
reflection groups,
intertwining operator
Received by editor(s):
May 7, 1996
Additional Notes:
Supported by the National Science Foundation under Grant DMS9500532
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1997
American Mathematical Society
