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On one set of orthogonal harmonic polynomials

Author(s): V. V. Karachik
Journal: Proc. Amer. Math. Soc. 126 (1998), 3513-3519.
MSC (1991): Primary 33D30; Secondary 33D25, 31B05
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Abstract: A new basis of harmonic polynomials is given. Proposed polynomials are orthogonal on the unit sphere and each term of this basis consists of monomials not present in the others.

References:

1.: E.M.Stein and G.Weiss, Introduction to Fourier Analysis on Euclidian Spaces, Princeton Univ. Press, Princeton, NJ, 1971. MR 46:4102
2.: V.V.Karachik, O polinomialnyh reshenijah sistem linejnyh differenzialnyh uravnenij, Voprosi Vychislitelnoy i prikladnoy matematiki 82 (1987), 41-48 (Russian).
3.: P.Pedersen, A basis for polynomial solutions to the systems of linear constant coefficient PDE's, Advances Math., Article No.0005 117 (1996), 157-163. MR 96k:35018
4.: H.Bateman and A.Erdélyi, Higher Transcendental Functions, vol. 2, New York, 1953.


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