Invariant differential operators on Hermitian symmetric spaces and their eigenvalues

Israel Journal of Mathematics

Volumn 119, Issue , 2000, Pages 157-185

  Zhang, Genkai ^a,b  

^a KARLSTAD UNIVERSITY   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012001743     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02810667     Document Type: Article

References (18)

1. M. Englis and J. Peetre, Covariant Laplacean operators on Kähler manifolds, Journal für die Reine und Angewandte Mathematik 478 (1996), 17-56.
2. J. Faraut and A. Koranyi, Function spaces and reproducing kernels on bounded symmetric domains, Journal of Functional Analysis 88 (1990), 64-89.
3. S. Helgason, Groups and Geometric Analysis, Academic Press, New York, London, 1984.
4. S. Helgason, Some results on invariant differential operators on symmetric spaces, American Journal of Mathematics 114 (1992), 789-811.
5. L. K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, American Mathematical Society, Providence, Rhode Island, 1963.
6. O. Loos, Bounded symmetric domains and Jordan pairs, University of California, Irvine, 1977.
7. B. Ørsted and G. Zhang, Weyl quantization and tensor products of Fock and Bergman spaces, Indiana University Mathematics Journal 43 (1994), 551-582.
8. J. Peetre and G. Zhang, Harmonic analysis on quantized Riemann sphere, International Journal of Mathematics and Mathematical Sciences 16 (1993), 225-244.
9. n, The Michigan Mathematical Journal 45 (1998), 387-397.
10. n, Springer-Verlag, Berlin, 1980.
11. I. Satake, Algebraic Structures of Symmetric Domains, Iwanami Shoten and Princeton University Press, Tokyo and Princeton, NJ, 1980.
12. W. Schmid, Die randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Inventiones Mathematicae 9 (1969), 61-80.
13. G. Shimura, Differential operators and the singular values of Eisenstein series, Duke Mathematical Journal 51 (1984), 261-329.
14. G. Shimura, Invariant differential operators on Hermitian symmetric spaces, Annals of Mathematics 132 (1990), 237-272.
15. G. Shimura, Differential operators, holomorphic projection, and singular forms, Duke Mathematical Journal 76 (1994), 141-173.
16. A. Unterberger and H. Upmeier, The Berezin transform and invariant differential operators, Communications in Mathematical Physics 164 (1994), 563-597.
17. H. Upmeier, Toeplitz operators on bounded symmetric domains, Transactions of the American Mathematical Society 280 (1983), 221-237.
18. H. Upmeier, Jordan algebras in analysis, operator theory, and quantum mechanics, Regional Conference Series in Mathematics No. 67, American Mathematical Society, Providence, 1987.