|
|
|
|
Литература
|
|
| |
| 1. |
G. E. Andrews, R. Askey, R. Roy, Special Functions, Cambridge Univ. Press, Cambridge, 1999   |
| 2. |
A. Borodin, G. Olshanski, “Harmonic functions on multiplicative graphs and interpolation polynomials”, Electr. J. Combin., 7 (2000), #R28 |
| 3. |
A. Borodin, G. Olshanski, “The Young bouquet and its boundary”, Moscow Math. J., 13:2 (2013), 193–232   |
| 4. |
P. J. Forrester, S. Ole Warnaar, “The importance of Selberg integral”, Bull. Amer. Math. Soc. (N.S.), 45 (2008), 489–534  |
| 5. |
V. Gorin, G. Olshanski, “Determinantal measures related to big $q$-Jacobi polynomials”, Funct. Anal. Appl., 49:3 (2015), 214–217 |
| 6. |
V. Gorin, G. Olshanski, “A quantization of the harmonic analysis on the infinite-dimensional unitary group”, J. Funct. Anal., 270:1 (2016), 376–418 ; arXiv: 1504.06832 |
| 7. |
G. Heckman, “Hypergeometric and spherical functions”: G. Heckman, H. Schlichtkrull, Harmonic Analysis and Special Functions on Symmetric Spaces, Academic. Press, San Diego, 1994 |
| 8. |
K. W. J. Kadell, “The Selberg–Jack symmetric functions”, Adv. Math., 130:1 (1997), 33–102 |
| 9. |
S. V. Kerov, “Anisotropic Young diagrams and Jack symmetric functions”, Funct. Anal. Appl., 34:1 (2000), 41–51 |
| 10. |
T. H. Koornwinder, “Special functions associated with root systems: A first introduction for nonspecialists”, Special Functions and Differential Equations, eds. K. Srinivasa Rao et al., Allied Publishers, Madras, 1998, 10–24 |
| 11. |
M. Lassalle, “Polynômes de Jacobi généralisés”, C. R. Acad. Sci. Paris Sér. I Math., 312:6 (1991), 425–428 |
| 12. |
I. G. Macdonald, Orthogonal polynomials associated with root systems, Preprint, 1987 ; reproduced in: Séminaire Lotharingien de Combinatoire, 45 (2000), Article B45a |
| 13. |
K. Mimachi, “A duality of the Macdonald–Koornwinder polynomials and its application to integral representations”, Duke Math. J., 107:2 (2001), 265–281 |
| 14. |
Yu. A. Neretin, “Hua-type integrals over unitary groups and over projective limits of unitary groups”, Duke Math. J., 114 (2002), 239–266 |
| 15. |
A. Okounkov, G. Olshanski, “Limits of $BC$-type orthogonal polynomials as the number of variables goes to infinity”, Jack, Hall–Littlewood and Macdonald polynomials, Contemp. Math., 417, Amer. Math. Soc., Providence, RI, 2006, 281–318 |
| 16. |
G. Olshanski, “The problem of harmonic analysis on the infinite-dimensional unitary group”, J. Funct. Anal., 205:2 (2003), 464–524 |
| 17. |
G. Olshanski, “Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities”, Funct. Anal. Appl., 37:4 (2003), 281–301 |
| 18. |
G. Olshanski, A. Osinenko, “Multivariate Jacobi polynomials and the Selberg integral”, Funct. Anal. Appl., 46:4 (2012), 262–278  |
| 19. |
D. Pickrell, “Measures on infinite dimensional Grassmann manifold”, J. Funct. Anal., 70 (1987), 323–356 |
| 20. |
E. M. Rains, “$BC_n$-symmetric polynomials”, Transform. Groups, 10:1 (2005), 63–132 |
