On one set of orthogonal harmonic polynomials
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- by V. V. Karachik PDF
- Proc. Amer. Math. Soc. 126 (1998), 3513-3519 Request permission
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
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
- V.V.Karachik, O polinomialnyh reshenijah sistem linejnyh differenzialnyh uravnenij, Voprosi Vychislitelnoy i prikladnoy matematiki 82 (1987), 41–48 (Russian).
- 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, DOI 10.1006/aima.1996.0005
- H.Bateman and A.Erdélyi, Higher Transcendental Functions, vol. 2, New York, 1953.
Additional Information
- V. V. Karachik
- Affiliation: Institute of Cybernetics of Academy of Science of Uzbekistan, 34, F.Hodzhaev St., Tashkent, 700143, Uzbekistan
- ORCID: 0000-0002-3077-3595
- Email: karachik@uwed.freenet.uz
- Received by editor(s): December 3, 1996
- Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3513-3519
- MSC (1991): Primary 33D30; Secondary 33D25, 31B05
- DOI: https://doi.org/10.1090/S0002-9939-98-05019-9
- MathSciNet review: 1621957