Analysis in Theory and Applications

, Volume 19, Issue 3, pp 234–237 | Cite as

On a set ofh-harmonic homogeneous polynomials

  • Wang Renhong
  • Zhou Heng


In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x(d))=x 1 2k ...x d 2k on Sd−1. We obtain the explicit formula on a basis of the orthogonal homogeneous polynomials of degree n. It is simpler than the formula in [2], and can be regarded as an extension of [1] under the weighted case.

Key Words

h-harmonic homogeneous polynomials weight functions 

AMS(2000) subject classification

43C05 33C55 


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  1. [1]
    Karachik, V. V., On One Set of Orthogonal Harmonic Polynomials, Proc. Amer. Math. Soc., 12(1998), No. 126, 3513–3519.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Dunkl, C. F. and Xu, Y., Orthogonal Polynomials of Several Variables, Cambridge Univ. Press, 2001.Google Scholar
  3. [3]
    Dunkl, C. F., Differential-Difference Operators Associated to Reflection Groups. Trans. Amer. Math. Soc., 311(1989), 167–183.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 2003

Authors and Affiliations

  • Wang Renhong
    • 1
  • Zhou Heng
    • 1
  1. 1.Institute of Mathematical SciencesDalian University of TechnologyDalianP. R. China

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