Geodesic
On differential operators for Chebyshev polynomials of several variables
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 25, Tome 473 (2018), pp. 99-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We obtain the differential operators for bivariate Chebyshev polynomials of the first kind, associated with root systems of the simple Lie algebras $C_2$ and $G_2$. 
@article{ZNSL_2018_473_a6,
     author = {E. V. Damaskinskiy and M. A. Sokolov},
     title = {On differential operators for {Chebyshev} polynomials of several variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--109},
     year = {2018},
     volume = {473},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_473_a6/}
}
TY  - JOUR
AU  - E. V. Damaskinskiy
AU  - M. A. Sokolov
TI  - On differential operators for Chebyshev polynomials of several variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 99
EP  - 109
VL  - 473
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_473_a6/
LA  - ru
ID  - ZNSL_2018_473_a6
ER  - 
%0 Journal Article
%A E. V. Damaskinskiy
%A M. A. Sokolov
%T On differential operators for Chebyshev polynomials of several variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 99-109
%V 473
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_473_a6/
%G ru
%F ZNSL_2018_473_a6
E. V. Damaskinskiy; M. A. Sokolov. On differential operators for Chebyshev polynomials of several variables. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 25, Tome 473 (2018), pp. 99-109. http://geodesic.mathdoc.fr/item/ZNSL_2018_473_a6/

[1] T. H. Koornwinder, “Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators I–IV”, Indagationes Mathematicae, 77 (1974), 48–66 ; 357–381 | DOI | MR | Zbl | Zbl

[2] T. H. Koornwinder, “Two-variable analogues of the classical orthogonal polynomials”, Theory and application of special functions, ed. R. A. Askey, Academic Press, 1975, 435–495 | DOI | MR

[3] G. J. Heckman, “Root systems and hypergeometric functions: II”, Comp. Math., 64 (1987), 353–373 | MR | Zbl

[4] M. E. Hoffman, W. D. Withers, “Generalized Chebyshev polynomials associated with affine Weyl groups”, Trans. Am. Math. Soc., 308 (1988), 91–104 | DOI | MR | Zbl

[5] R. J. Beerends, “Chebyshev polynomials in several variables and the radial part Laplace–Beltrami operator”, Trans. Am. Math. Soc., 328 (1991), 770–814 | DOI | MR

[6] A. Klimyk, J. Patera, “Orbit functions”, SIGMA, 4 (2006), 002 | MR

[7] Ken B. Dunn, Rudolf Lidl, “Generalizations of the classical Chebyshev polynomials to polynomials in two variables”, Cz. Math. J., 32 (1982), 516–528 | MR | Zbl

[8] T. Rivlin, The Chebyshev Polynomials, Wiley-Interscience publication, New York, 1974 | MR | Zbl

[9] N. N. Lebedev, Spetsialnye funktsii i ikh prilozheniya, FML, 1963

[10] P. K. Suetin, Ortogonalnye mnogochleny po dvum peremennym, FM, 1988