Berezin transform on compact Hermitian symmetric spaces

Manuscripta Mathematica

Volumn 97, Issue 3, 1998, Pages 371-388

  Zhang, Genkai ^a  

^a KARLSTAD UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032210377     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002290050109     Document Type: Article

References (20)

1. Berezin, F.A.: General concept of quantization. Commun. Math. Phys. 40, 153-174 (1975)
2. Brussee, R., Heckman, G.J. and Opdam, E.M.: Variation of a theme of MacDonald. Math. Z. 208, 1-10 (1991)
3. Cahen, M., Gutt, S. and Rawnsley, J.: Quantization of Kähler manifolds II. Trans. Am. Math. Soc. 337, 73-98 (1993)
4. Debiard, A.: Système Différentiel hypergéométrique et parties radiales des opérateurs invariants des espaces. In: Séminaire d́algèbre Paul Dubreil et Marie-Paule Malliavian, Lecture Notes in Math., No. 1296, pp. 42-123
5. Erdelyi, A. et al: Higher transdental functions. 1, New York-Toronto-London: McGraw-Hill, 1953
6. FK] Faraut, J. and Koranyi, A.: Function spaces and reproducing kernels on bounded symmetric domains. J. Func. Anal. 89, 64-89 (1990)
7. Heckman, G.J.: An elementary approach to the hypergeometric shift operator of Opdam. Invent. Math. 103, 341-350 (1991)
8. Heckman, G.J.: Root systems and hypergeometric functions II. Compositio Math. 64, 353-373 (1987)
9. Heckman, G.J. and Opdam, E.M.: Root systems and hypergeometric functions I. Compositio Math. 64, 329-352 (1987)
10. Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. London: Academic Press, 1978
11. Helgason, S.: Groups and geometric analysis. London: Academic Press, 1984
12. Loos, O.: Bounded Symmetric Domains and Jordan Pairs. University of California, Irvine, 1977
13. Peetre, J.: Berezin transform and Haplitz opertors. J. Oper. Theory 24, 165-168 (1990)
14. Peetre, J. and Zhang, G.: A weighted Plancherel formula III. The case of a hyperbolic matrix ball. Collect. Math. 43, 273-301 (1992)
15. OØrsted, B. and Zhang, G.: Weyl Quantization and Tensor products of Fock and Bergman spaces. Indiana Univ. Math. J. 43, 551-582 (1994)
16. Satake, I.: Algebraic structures of symmetric domains. Tokyo and Princeton, NJ.: Iwanami Shoten and Princeton Univ. Press, 1980
17. Unterberger, A. and Upmeier, H.: Berezin transform and invariant differential operators. Commun. Math. Phys. 164(3), 563-597 (1994)
18. Upmeier, H.: Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics. CBMS Conference Series No. 67, Am. Math. Soc., 1987
19. Vretare, L.: Elementary spherical functions on symmetric spaces. Math. Scand. 39, 343-358 (1976)
20. Zelobenko, D.P.: Compact Lie groups and their representations. Providence, R.I.: Am. Math. Soc. Transl. Math. Monographs, vol. 40, 1973