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On one set of orthogonal
harmonic polynomials

Author: V. V. Karachik
Journal: Proc. Amer. Math. Soc. 126 (1998), 3513-3519
MSC (1991): Primary 33D30; Secondary 33D25, 31B05
MathSciNet review: 1621957
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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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Additional Information

V. V. Karachik
Affiliation: Institute of Cybernetics of Academy of Science of Uzbekistan, 34, F.Hodzhaev St., Tashkent, 700143, Uzbekistan

Keywords: Harmonic polynomials, orthogonality
Received by editor(s): December 3, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society

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