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Hypergeometric functions on complex matrix space
Author(s):
Kenneth I.
Gross;
Donald St. P.
Richards
Journal:
Bull. Amer. Math. Soc.
24
(1991),
349-355.
MSC (1985):
Primary 22E30, 33A75, 43A85, 62H10;
Secondary 20G20, 32A07, 44A10, 62E15
MathSciNet review:
1071029
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References |
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Additional information
References:
- 1.
- H. Ding, Operator-valued Bessel functions on Schrödinger-Fock spaces and Siegel domains of type. II, preprint. MR 1712918
- 2.
- H. Ding, Operator-valued Bessel functions on Schrödinger II: holomorphic discrete series and harmonic representations (in preparation).
- 3.
- H. Ding and K. I. Gross, Operator-valued Bessel functions on symmetric cones and holomorphic discrete series (in preparation).
- 4.
- J. Faraut and A. Korányi, Fonctions hypergéometriques associées aux cônes symétriques, C. R. Acad. Sci. Paris Sér. I 307 (1988), 555-558. MR 967360
- 5.
- K. I. Gross and R. A. Kunze, Generalized Fourier-Bessel transforms and holomorphic discrete series, Proc. Internat. Conf. in Harmonic Analysis, Lecture Notes in Math., vol. 261, Springer-Verlag, Berlin and New York, 1973, pp. 79-122. MR 486318
- 6.
- K. I. Gross and D. St. P. Richards, Special functions of matrix argument, I: Algebraic induction, zonal polynomials, and hypergeometric functions, Trans. Amer. Math. Soc. 301 (1987), 781-811. MR 882715
- 7.
- K. I. Gross and D. St. P. Richards, Total positivity, spherical series, and hypergeometric functions of matrix argument, J. Approximation Theory 59 (1989), 224-246. MR 1022118
- 8.
- K. I. Gross and D. St. P. Richards, Special functions of matrix argument, II: The fine structure of hypergeometric functions on complex matrix space (in preparation).
- 9.
- A. T. James, Distributions of matrix variates and latent roots derived from normal samples, Ann. of Math. Statistics 35 (1964), 475-501. MR 181057
- 10.
- A. Korányi, Hua-type integrals, hypergeometric functions, and symmetric polynomials, preprint. MR 1135834
- 11.
- D. St. P. Richards, Totally positive kernels, Pólya frequency functions, and generalized hypergeometric series, Linear Algebra Appl. 137/138 (1990), 467-478. MR 1067687
- 12.
- H. Weyl, The classical groups, Princeton Univ. Press, Princeton, NJ, 1939. MR 1488158
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22E30, 33A75, 43A85, 62H10, 20G20, 32A07, 44A10, 62E15
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22E30, 33A75, 43A85, 62H10, 20G20, 32A07, 44A10, 62E15
Additional Information:
DOI:
10.1090/S0273-0979-1991-16031-3
PII:
S 0273-0979(1991)16031-3
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