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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: 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. Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR 0304972
  • 2. V.V.Karachik, O polinomialnyh reshenijah sistem linejnyh differenzialnyh uravnenij, Voprosi Vychislitelnoy i prikladnoy matematiki 82 (1987), 41-48 (Russian).
  • 3. Paul S. Pedersen, A basis for polynomial solutions to systems of linear constant coefficient PDE’s, Adv. Math. 117 (1996), no. 1, 157–163. MR 1367588, 10.1006/aima.1996.0005
  • 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
Email: karachik@uwed.freenet.uz

DOI: https://doi.org/10.1090/S0002-9939-98-05019-9
Keywords: Harmonic polynomials, orthogonality
Received by editor(s): December 3, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society