|
|
|
|
References
|
|
| |
| 1. |
Andrews G. E., Askey R., Roy R., Special functions, Cambridge Univ. Press, 1999   |
| 2. |
Askey R., “An integral of Ramanujan and orthogonal polynomials”, J. Indian Math. Soc. (N.S.), 51 (1987), 27–36 |
| 3. |
Borodin A., Olshanski G., Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes, arXiv.org: math.RT/0109194 |
| 4. |
Borodin A., Olshanski G., Random partitions and the Gamma kernel, arXiv.org: math-ph/0305043 |
| 5. |
Dunford N., Schwartz J. T., Linear operators, vol. 2, Wiley & Sons, 1963 ; Danford M., Shvarts Dzh., Lineinye operatory, t. 2, Mir, M., 1966 |
| 6. |
Grunbaum F. A., Pacharoni I., Tirao J., “Matrix valued spherical functions associated to the complex projective plane”, J. Funct. Anal., 188:2 (2002), 350–441   |
| 7. |
Erdelyi A., Magnus W., Oberhetinger F., Tricomi F., Higher transcendental functions, vol. 1, 2, McGray–Hill, 1953 ; Erdei A., Magnus V., Oberkhetinger F., Trikomi F., Vysshie transtsendentnye funktsii, Nauka, M., 1966 |
| 8. |
Flensted-Jensen M., Koornwinder T., “The convolution structure for Jacobi function expansions”, Ark. Math., 11 (1973), 245–262 |
| 9. |
Groenevelt W., The Wilson function transform, arXiv.org: math.CA/0306424 |
| 10. |
Kamke E., Differentialgleichungen. I. Gevöhnliche Differentialgleichungen, 6 ed., Leipzig, 1959 ; Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971 |
| 11. |
Koekoek R., Swarttouw R. F., The Askey-scheme of hypergeometric orthogonal polynomials and its $q$-analogue, Report no. 94-05
http://aw.twi.tudelft.nl/~koekoek/askey.html, Delft University of Technology, Faculty of Technical Mathematics and Informatics, 1994 |
| 12. |
Koornwinder T. H., “A new proof of a Paley–Wiener theorem for Jacobi transform”, Ark. Math., 13 (1975), 145–159 |
| 13. |
Koornwinder T. H., “Jacobi functions and analysis on noncompact symmetric spaces”, Special functions: group theoretical aspects and applications, eds. Askey R., Koornwinder T., Reidel, Dodrecht–Boston, 1984, 1–85 |
| 14. |
Lesky P. A., “Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen”, Z. Angew. Math. Mech., 76:3 (1996), 181–184 |
| 15. |
Lesky P. A., “Unendliche und endliche Orthogonalsysteme von continuous Hahnpolynomen”, Results Math., 31:1–2 (1997), 127–135 |
| 16. |
Lesky P. A., Waibel B.-M., “Orthogonalitat von Racahpolynomen und Wilsonpolynomen”, Results Math., 35:1–2 (1999), 119–133 |
| 17. |
Molchanov V. F., “Tenzornye proizvedeniya unitarnykh predstavlenii trekhmernoi gruppy Lorentsa”, Izv. AN SSSR, ser. mat., 43 (1979), 860–891  |
| 18. |
Molchanov V. F., “Formula Plansherelya dlya psevdorimanovykh simmetricheskikh prostranstv ranga 1”, DAN SSSR, 290:3 (1986), 545–549 |
| 19. |
Molchanov V. F., “Garmonicheskii analiz na odnorodnykh prostranstvakh”, Nekommutativnyi garmonicheskii analiz-II, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 59, VINITI, M., 1990, 5–144 |
| 20. |
Neretin Yu. A., “Indeksnoe gipergeometricheskoe preobrazovanie i imitatsiya
analiza yader Berezina na giperbolicheskikh prostranstvakh”, Matem. sb., 192:3 (2001), 83–114 ; arXiv.org: math/0104035 |
| 21. |
Neretin Yu. A., “Beta-integraly i konechnye ortogonalnye sistemy mnogochlenov Vilsona”, Matem. sb., 193:7 (2002), 131–148 |
| 22. |
Neretin Yu. A., Perturbations of some classical hypergeometric orthogonal systems, arXiv.org: math/a0309445 |
| 23. |
Olevskii M. N., “O predstavlenii proizvolnoi funktsii v vide integrala
s yadrom, yavlyayuschimsya gipergeometricheskoi funktsiei”, DAN SSSR, 69:1 (1949), 11–14 |
| 24. |
Peetre J., “Correspondence principle for the quantized annulus, Romanovski polynomials, and Morse potential”, J. Funct. Anal., 117:2 (1993), 377–400 |
| 25. |
Prudnikov A. M., Brychkov Yu. A., Marichev O. I., Integraly i ryady, t. 1–3, Nauka, M., 1981, 1983, 1986 |
| 26. |
Pukanszky L., “On the Kronecker products of irreducible unitary
representations of the $2\times2$ real unimodular group”, Trans. Amer. Math. Soc., 100 (1961), 116–152 |
| 27. |
Romanovski V. I., “Sur quelques classes nouwels of polynomes orthogonaux”, C. R. Acad. Sci. Paris, 188 (1929), 1023–1025 |
| 28. |
Rosengren H., “Multilinear Hankel forms of higher order and orthogonal polynomials”, Math. Scand., 82:1 (1998), 53–88 |
| 29. |
Rosengren H., “Multivariable orthogonal polynomials and coupling
coefficients for discrete series representations”, SIAM J. Math. Anal., 30 (1999), 233–272 |
| 30. |
Tirao J. A., “The matrix-valued hypergeometric equation”, Proc. Natl. Acad. Sci. USA, 100:14 (2003), 8138–8141  |
| 31. |
Titchmarsh E. C., Eigenfunction expansions with second-order differential operators, v. 1, Clarendon Press, Oxford, 1946 ; Titchmarsh E., Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, t. 1, IL, M., 1960 |
| 32. |
Vilenkin N. Ya., Klimyk A. U., Representations of Lie groups and special functions, vol. 1, 2, Kluwer, 1991 |
| 33. |
Weyl H., “Uber gewonliche lineare Differentialgleichungen mis
singularen Stellen und ihre Eigenfunktionen (2 Note)”, Nachr. Konig. Gess. Wissen. Göttingen. Math.-Phys., 1910, 442–467 ; Reprinted in Weyl H., Gessamelte Abhandlungen, Bd. 1, Springer-Verlag, 1968, 222–247 |
| 34. |
Zhang Gen Kai, “Tensor products of weighted Bergman spaces and invariant Ha-plitz operators”, Math. Scand., 71:1 (1992), 85–95 |
