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On Differential Operators for Chebyshev Polynomials in Several Variables

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We obtain differential operators for the bivariate Chebyshev polynomials of the first kind associated with the root systems of the simple Lie algebras C2 and G2.

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References

  1. T. H. Koornwinder, “Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, I–IV,” Indag. Math., 77, 48–66, 357–381 (1974).

    Article  MathSciNet  Google Scholar 

  2. T. H. Koornwinder, “Two-variable analogues of the classical orthogonal polynomials,” in: R. A. Askey (ed.), Theory and Application of Special Functions, Academic Press (1975), pp. 435–495.

  3. G. J. Heckman, “Root systems and hypergeometric functions: II,” Compos. Math., 64, 353–373 (1987).

    MathSciNet  MATH  Google Scholar 

  4. M. E. Hoffman and W. D. Withers, “Generalized Chebyshev polynomials associated with affine Weyl groups,” Trans. Amer. Math. Soc., 308, 91–104 (1988).

    Article  MathSciNet  Google Scholar 

  5. R. J. Beerends, “Chebyshev polynomials in several variables and the radial part of the Laplace–Beltrami operator,” Trans. Amer. Math. Soc., 328, 770–814 (1991).

    Article  MathSciNet  Google Scholar 

  6. A. Klimyk and J. Patera, “Orbit functions,” SIGMA, 2, 006 (2006).

    MathSciNet  MATH  Google Scholar 

  7. K. B. Dunn and R. Lidl, “Generalizations of the classical Chebyshev polynomials to polynomials in two variables,” Czechoslovak. Math. J., 32, 516–528 (1982).

    MathSciNet  MATH  Google Scholar 

  8. T. Rivlin, The Chebyshev Polynomials, Wiley-Interscience, New York (1974).

    MATH  Google Scholar 

  9. N. N. Lebedev, Special Functions and Their Applications, Prentice-Hall (1965).

  10. P. K. Suetin, Orthogonal Polynomials in Two Variables, CRC Press (1999).

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Authors and Affiliations

  1. Military Engineering–Technical University, St. Petersburg, Russia

    E. V. Damaskinsky

  2. Military Academy of Communications, St. Petersburg, Russia

    M. A. Sokolov

Authors
  1. E. V. Damaskinsky
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  2. M. A. Sokolov
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Correspondence to E. V. Damaskinsky.

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Dedicated to M. A. Semenov-Tian-Shansky on the occasion of his 70th birthday

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 473, 2018, pp. 99–109.

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Damaskinsky, E.V., Sokolov, M.A. On Differential Operators for Chebyshev Polynomials in Several Variables. J Math Sci 242, 651–657 (2019). https://doi.org/10.1007/s10958-019-04504-6

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  • DOI: https://doi.org/10.1007/s10958-019-04504-6

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