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Volumn 348, Issue 2, 1996, Pages 411-479

Berezin quantization and reproducing kernels on complex domains

Author keywords

Asymptotic behaviour; Berezin transform; Complex ellipsoids; Covariant symbols of operators; K hler manifolds; K hler Einstein metric; Pseudoconvex domains; Quantization; Reproducing (Bergman) kernels; Weighted Bergman spaces

Indexed keywords


EID: 21344458987     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01551-6     Document Type: Article
Times cited : (81)

References (41)
  • 3
    • 84927987695 scopus 로고
    • Quantization in complex symmetric spaces
    • [Ber2] MR 58:22691
    • [Ber2] F.A. Berezin, Quantization in complex symmetric spaces, Math. USSR Izvestiya 9 (1975), 341-379. MR 58:22691
    • (1975) Math. USSR Izvestiya , vol.9 , pp. 341-379
    • Berezin, F.A.1
  • 4
    • 84967735784 scopus 로고
    • Toeplitz operators on the Segal-Bargmann space
    • [BC1] MR 88c:47044
    • [BC1] C.A. Berger and L.A. Coburn, Toeplitz operators on the Segal-Bargmann space, Trans. Amer.Math. Soc. 301 (1987), 813-829. MR 88c:47044
    • (1987) Trans. Amer.Math. Soc. , vol.301 , pp. 813-829
    • Berger, C.A.1    Coburn, L.A.2
  • 5
    • 0001299191 scopus 로고
    • Heat flow and Berezin-Toeplitz estimates
    • [BC2] MR 95g:47038
    • [BC2] C.A. Berger and L.A. Coburn, Heat flow and Berezin-Toeplitz estimates, Amer. J.Math. 116 (1994), 563-590. MR 95g:47038
    • (1994) Amer. J.Math. , vol.116 , pp. 563-590
    • Berger, C.A.1    Coburn, L.A.2
  • 6
    • 0001724629 scopus 로고
    • Function theory on Carton domains and the Berezin-Toeplitz symbol calculus
    • [BCZ] MR 89m:32053
    • [BCZ] C.A. Berger, L.A. Coburn and K.H. Zhu, Function theory on Carton domains and the Berezin-Toeplitz symbol calculus, Amer. J.Math. 110 (1988), 921-953. MR 89m:32053
    • (1988) Amer. J.Math. , vol.110 , pp. 921-953
    • Berger, C.A.1    Coburn, L.A.2    Zhu, K.H.3
  • 7
    • 0011608601 scopus 로고
    • The kernel function and conformal mapping
    • [Berg] AMS, Providence, MR 12:402
    • [Berg] S. Bergman, The kernel function and conformal mapping, Math. Surveys, vol. 5, AMS, Providence, 1950. MR 12:402
    • (1950) Math. Surveys , vol.5
    • Bergman, S.1
  • 9
    • 0000254883 scopus 로고
    • Non-perturbative deformation quantization on Carton domains
    • [BLU] MR 94d:47065
    • [BLU] D. Borthwick, A. Lesniewski, H. Upmeier, Non-perturbative deformation quantization on Carton domains, J. Funct. Anal. 113 (1993), 153-176. MR 94d:47065
    • (1993) J. Funct. Anal. , vol.113 , pp. 153-176
    • Borthwick, D.1    Lesniewski, A.2    Upmeier, H.3
  • 10
    • 45149137712 scopus 로고
    • Quantization of Kähler manifolds, I: Geometric interpretation of Berezin's quantization
    • [CGR]
    • [CGR] M. Cahen, S. Gutt, J. Rawnsley, Quantization of Kähler manifolds, I: Geometric interpretation of Berezin's quantization, J. Geom. Physics 7 (1990), 45-62;
    • (1990) J. Geom. Physics , vol.7 , pp. 45-62
    • Cahen, M.1    Gutt, S.2    Rawnsley, J.3
  • 12
    • 51249161491 scopus 로고
    • MR 92e:58082, 93i:58063; 95c:58082
    • III, Letters in Math. Phys. 30 (1994), 291-305. MR 92e:58082, 93i:58063; 95c:58082
    • (1994) III, Letters in Math. Phys. , vol.30 , pp. 291-305
  • 13
    • 84980167518 scopus 로고
    • On the existence of a complete Kähler-Einstein metric on non-compact complex manifolds and the regularity of Fefferman's equation
    • [ChY] MR 82f:53074
    • [ChY] S.Y. Cheng, S.-T. Yau, On the existence of a complete Kähler-Einstein metric on non-compact complex manifolds and the regularity of Fefferman's equation, Comm. Pure Appl.Math. 33 (1980), 507-544. MR 82f:53074
    • (1980) Comm. Pure Appl.Math. , vol.33 , pp. 507-544
    • Cheng, S.Y.1    Yau, S.-T.2
  • 14
    • 0042419882 scopus 로고
    • Berezin-Toeplitz quantization
    • [C1] Birkhauser, MR 95f:47046
    • [C1] L.A. Coburn, Berezin-Toeplitz quantization, in: Algebraic methods in Operator Theory, Birkhauser, 1994, pp. 101-108. MR 95f:47046
    • (1994) Algebraic Methods in Operator Theory , pp. 101-108
    • Coburn, L.A.1
  • 15
    • 34249840494 scopus 로고
    • Deformation estimates for the Berezin-Toeplitz quantization
    • [C2] MR 93j:47038
    • [C2] L.A. Coburn, Deformation estimates for the Berezin-Toeplitz quantization, Comm.Math. Phys. 149 (1992), 415-424. MR 93j:47038
    • (1992) Comm.Math. Phys. , vol.149 , pp. 415-424
    • Coburn, L.A.1
  • 16
    • 21844492140 scopus 로고
    • Toeplitz algebras and Rieffel deformations
    • [CX]
    • [CX] L.A. Coburn, J. Xia, Toeplitz algebras and Rieffel deformations, Comm.Math. Phys. 168 (1995), 23-38.
    • (1995) Comm.Math. Phys. , vol.168 , pp. 23-38
    • Coburn, L.A.1    Xia, J.2
  • 17
    • 0001341127 scopus 로고
    • Regularity theorems in geometry
    • [DK] MR 83f:53018
    • [DK] D.M. DeTurck, J.L. Kazdan, Regularity theorems in geometry, Ann. Sci. Ecole Norm. Sup. 14 (1981), 249-260. MR 83f:53018
    • (1981) Ann. Sci. Ecole Norm. Sup. , vol.14 , pp. 249-260
    • DeTurck, D.M.1    Kazdan, J.L.2
  • 18
    • 0039891912 scopus 로고
    • Density of algebras generated by Toeplitz operators on Bergman spaces
    • [E1] MR 95e:47036
    • [E1] M. Engliš, Density of algebras generated by Toeplitz operators on Bergman spaces, Arkiv for Matematik 30 (1992), 227-243. MR 95e:47036
    • (1992) Arkiv for Matematik , vol.30 , pp. 227-243
    • Engliš, M.1
  • 19
    • 25444475666 scopus 로고
    • Asymptotics of reproducing kernels on a plane domain
    • [E2]
    • [E2] M. Engliš, Asymptotics of reproducing kernels on a plane domain, Proceedings Amer.Math. Soc. 123 (1995), 3157-3160.
    • (1995) Proceedings Amer.Math. Soc. , vol.123 , pp. 3157-3160
    • Engliš, M.1
  • 20
    • 84974002911 scopus 로고
    • Asymptotics of the Berezin transform and quantization on planar domains
    • [E3]
    • [E3] M. Englis, Asymptotics of the Berezin transform and quantization on planar domains, Duke Math. J. 79 (1995), 57-76.
    • (1995) Duke Math. J. , vol.79 , pp. 57-76
    • Englis, M.1
  • 21
    • 84974001943 scopus 로고    scopus 로고
    • On. the correspondence principle for the quantized annulus
    • [EP] to appear
    • [EP] M. Engliš, J. Peetre, On. the correspondence principle for the quantized annulus, Math. Scand. (to appear).
    • Math. Scand.
    • Engliš, M.1    Peetre, J.2
  • 22
    • 0001768923 scopus 로고
    • Function spaces and reproducing kernels on bounded symmetric domains
    • [FK1] MR 90m:32049
    • [FK1] J. Faraut, A. Korányi, Function spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal. 88 (1990), 64-89. MR 90m:32049
    • (1990) J. Funct. Anal. , vol.88 , pp. 64-89
    • Faraut, J.1    Korányi, A.2
  • 27
    • 34249832301 scopus 로고
    • Quantum Riemann surfaces, I: The unit disc
    • [KL]
    • [KL] S. Klimek, A. Lesniewski, Quantum Riemann surfaces, I: The unit disc, Comm.Math. Phys. 146 (1992), 103-122;
    • (1992) Comm.Math. Phys. , vol.146 , pp. 103-122
    • Klimek, S.1    Lesniewski, A.2
  • 28
    • 0007746339 scopus 로고
    • II: The discrete series
    • MR 93g:58009; 93k:58011
    • II: The discrete series, Letters in Math. Phys. 24 (1992), 125-139. MR 93g:58009; 93k:58011
    • (1992) Letters in Math. Phys. , vol.24 , pp. 125-139
  • 30
    • 0001604730 scopus 로고
    • Convexity in complex analysis, in: Several complex variables and complex geometry, part 1
    • [Krn] E. Bedford, J.P. D'Angelo, R.E. Greene, S.G. Krantz, eds.
    • [Krn] S.G. Krantz, Convexity in complex analysis, in: Several complex variables and complex geometry, part 1 (E. Bedford, J.P. D'Angelo, R.E. Greene, S.G. Krantz, eds.), Proc. Symposia Pure Math., vol. 52, 1994, pp. 119-138.
    • (1994) Proc. Symposia Pure Math. , vol.52 , pp. 119-138
    • Krantz, S.G.1
  • 32
    • 33645942409 scopus 로고
    • Complete Kähler-Einstein metrics on bounded domains locally of finite volume at some boundary points
    • [M] MR 89m:32029
    • [M] N.Mok, Complete Kähler-Einstein metrics on bounded domains locally of finite volume at some boundary points, Math. Ann. 281 (1988), 23-30. MR 89m:32029
    • (1988) Math. Ann. , vol.281 , pp. 23-30
    • Mok, N.1
  • 33
    • 0002433346 scopus 로고
    • Completeness of Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions
    • [MY] MR 85j:53068
    • [MY] N.Mok, S.-T. Yau, Completeness of Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions, Proc. Symposia in Pure Mathematics, vol. 39, part 1, 1983, pp. 41-59. MR 85j:53068
    • (1983) Proc. Symposia in Pure Mathematics , vol.39 , Issue.1 PART , pp. 41-59
    • Mok, N.1    Yau, S.-T.2
  • 34
    • 0000313827 scopus 로고
    • *-products on some Kähler manifolds
    • [Mor] MR 88c:58021
    • [Mor] C.Moreno, *-products on some Kähler manifolds, Letters Math. Phys. 11 (1986), 361-372. MR 88c:58021
    • (1986) Letters Math. Phys. , vol.11 , pp. 361-372
    • Moreno, C.1
  • 35
    • 0001514527 scopus 로고
    • The Berezin transform and Ha-plitz operators
    • [Pe1] MR 91k:47058
    • [Pe1] J. Peetre, The Berezin transform and Ha-plitz operators, J. Operator Theory 24 (1990), 165-168. MR 91k:47058
    • (1990) J. Operator Theory , vol.24 , pp. 165-168
    • Peetre, J.1
  • 36
    • 38248998622 scopus 로고
    • Correspondence principle for quantized annulus, Romanowski polynomials, Morse potential
    • [Pe2] MR 94m:47056
    • [Pe2] J. Peetre, Correspondence principle for quantized annulus, Romanowski polynomials, Morse potential, J. Funct. Anal. 117 (1993), 377-400. MR 94m:47056
    • (1993) J. Funct. Anal. , vol.117 , pp. 377-400
    • Peetre, J.1
  • 37
    • 0002538522 scopus 로고
    • Quantization and C*-algebras
    • [Riel] AMS, MR95h:46108
    • [Riel] M.A. Rieffel, Quantization and C*-algebras, Contemp.Math., vol. 167, AMS, 1994, pp. 66-97. MR95h:46108
    • (1994) Contemp.Math. , vol.167 , pp. 66-97
    • Rieffel, M.A.1
  • 39
    • 0004093385 scopus 로고
    • Biholomorphic invariants related to the Bergman function
    • [Skw] MR 82e:32038
    • [Skw] M. Skwarczynski, Biholomorphic invariants related to the Bergman function, Dissertationes Math. 173 (1980). MR 82e:32038
    • (1980) Dissertationes Math. , vol.173
    • Skwarczynski, M.1
  • 40
    • 84972529454 scopus 로고
    • Pseudo-conformal transformations onto circular domains
    • [Spr] MR 12:817
    • [Spr] G. Springer, Pseudo-conformal transformations onto circular domains, Duke Math. J. 18 (1951), 411-424. MR 12:817
    • (1951) Duke Math. J. , vol.18 , pp. 411-424
    • Springer, G.1
  • 41
    • 0001134743 scopus 로고
    • Holomorphic equivalence problem for bounded Reinhardt domains
    • [Su] MR 58:1211
    • [Su] T. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235 (1978), 111-128. MR 58:1211
    • (1978) Math. Ann. , vol.235 , pp. 111-128
    • Sunada, T.1


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