Berezin kernels of tube domains

Journal of Functional Analysis

Volumn 181, Issue 2, 2001, Pages 189-208

  Van Dijk, G ^a   Pevzner, M ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Berezin kernel; Causal symmetric spaces; Holomorphic discrete series representations; Jordan algebras

Indexed keywords

EID: 0000201634     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2000.3706     Document Type: Article

References (17)

1. p-estimates of spherical functions and mean-value property. Integral Equations Operator Theory. 23:1995;123-144
2. Berezin F. A. Quantization in complex symmetric space. Math. USSR Izv. 9:1975;341-379
3. Berezin F. A. A connection between the co- and contravariant symbols of operators on the classical complex symmetric spaces. Dokl. Akad. Nauk. USSR. 241:1978;15-17
4. Bertram W. Algebraic structures of Makarevič spaces I. Transformation Groups. 3:1998;3-32
5. van Dijk G. Group representations on spaces of distributions. Russian J. Math. Phys. 2:1994;57-68
6. van Dijk G. Canonical representations. Tambov Univ. Rep. 2:1997;350-367
7. Faraut J., Korányi A. Analysis on Symmetric Cones. Oxford Science Publications. 1994
8. Faraut J., Olafsson G. Causal semisimple symmetric spaces, the geometry and harmonic analysis. Hofmann, Lawson, Vinberg. Semigroups in Algebra, Geometry and Analysis. 1995;De Gruyter, Berlin
9. S. C. Hille, Canonical representations associated to a character on a Hermitian symmetric space of rank one, preprint, Leiden University, 1996, Ph.D. thesis, Leiden University, 1999
10. Koufany K., Ørsted B. Function spaces on the Olshanskii semigroup and the Gel'fand-Gindikin program. Ann. Inst. Fourier. 46:1996;689-722
11. Yu. A. Neretin, Matrix analogs of B-function and Plancherel formula for Berezin kernel representations, preprint, 1999, http://xxx.lanl.gov/math.RT/9905045
12. Nomura T. Berezin transforms and group representations. J. Lie Theory. 8:1998;433-440
13. Ørsted B., Zhang G. Tensor products of analytic continuations of holomorphic discrete series. Canad. J. Math. 49:1997;1224-1241
14. G. Olafsson, and, B. Ørsted, Bargmann transform for symmetric spaces, preprint, 1999
15. Unterberger A., Upmeier H. The Berezin transform and invariant differential operators. Comm. Math. Phys. 164:1994;63-597
16. G. Zhang, Berezin transform on line bundles over bounded symmetric domains, preprint
17. G. Zhang, Berezin transform on real bounded symmetric domains, preprint