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We study the Berezin-Toeplitz quantization on Kaehler manifolds.
F. A. Berezin, Quantization , Izv. Akad. Nauk SSSR Ser. Mat. 38
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L. Boutet de Monvel and J. Sjöstrand, Sur la singularité des noyaux de Bergman et de Szegö , Astérisque, 34–35
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L. Boutet de Monvel and V. Guillemin, The spectral theory of Toeplitz operators , Annals of Mathematics Studies, vol. 99, Princeton University Press, Princeton, NJ, 1981
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M. De Wilde, P. Lecomte, Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds , Lett. Math. Phys. 7
1983
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G. Tian, On a set of polarized Kähler metrics on algebraic manifolds , J. Differential Geom. 32
1990
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N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators , Grundl. Math. Wiss. Band 298, Springer-Verlag, Berlin, 1992
1992
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M. Bordemann and E. Meinrenken and M. Schlichenmaier, Toeplitz quantization of Kähler manifolds and gl ( N ) {\rm gl}(N) , N → ∞ N\to\infty limits , Comm. Math. Phys. 165
1994
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B. V. Fedosov, Deformation quantization and index theory , Mathematical Topics, 9, Akademie Verlag, Berlin, 1996
1996
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1998
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D. Catlin, The Bergman kernel and a theorem of Tian , Analysis and geometry in several complex variables (Katata, 1997), Trends Math., Birkhäuser Boston, Boston, MA, 1999, pp. 1– 23
1999
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M. Engliš, The asymptotics of a Laplace integral on a Kähler manifold , J. Reine Angew. Math. 528
2000
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E. Hawkins, Geometric quantization of vector bundles and the correspondence with deformation quantization , Commun. Math. Phys., 215
2000
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Z. Lu, On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch , Amer. J. Math. 122
2000
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M. Schlichenmaier, Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization , Conférence Moshé Flato 1999, Vol. II (Dijon), Math. Phys. Stud., vol. 22, Kluwer Acad. Publ., Dordrecht, 2000, pp. 289–306
2000
Cited alongside, same era.
A. V. Karabegov and M. Schlichenmaier, Identification of Berezin-Toeplitz deformation quantization , J. Reine Angew. Math. 540
2001
Cited alongside, same era.
by same author, Weighted Bergman kernels and quantization , Commun. Math. Phys. 227
2002
Cited alongside, same era.
by same author, The first coefficients of the asymptotic expansion of the Bergman kernel of the spin c \text{spin}^{c} Dirac operator , Internat. J. Math. 17
2006
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P. Petersen, Riemannian geometry . Second edition. Graduate Texts in Mathematics, 171. Springer, New York, 2006. xvi+401 pp
2006
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K. Liu and X. Ma, A remark on ‘some numerical results in complex differential geometry’ , Math. Res. Lett. 14
2007
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X. Ma and G. Marinescu, Holomorphic Morse inequalities and Bergman kernels , Progress in Mathematics, vol. 254, Birkhäuser Boston Inc., Boston, MA, 2007, 422 pp
2007
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by same author, Asymptotic of the operators Q k Q_{k} , (2008), Appendix to [ 16 ]
2008
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L. Charles, Berezin-Toeplitz operators, a semi-classical approach , Comm. Math. Phys. 239
2003
Cited alongside, same era.
L. Wang, Bergman kernel and stability of holomorphic vector bundles with sections , MIT Ph.D. Dissertation (2003), 85 pages
2003
Cited alongside, same era.
X. Dai, K. Liu, and X. Ma, On the asymptotic expansion of Bergman kernel , J. Differential Geom. 72
2004
Cited alongside, same era.
by same author, Generalized Bergman kernels on symplectic manifolds , Adv. Math. 217
2004
Cited alongside, same era.
X. Wang, Canonical metrics on stable vector bundles , Comm. Anal. Geom. 13
2005
Cited alongside, same era.
by same author, Black holes and balanced metrics , arXiv: 0811.0367
Cited in the paper.
by same author, Quantisation and the Hessian of Mabuchi energy , arXiv: 1009.4543
Cited in the paper.
by same author, Toeplitz operators on symplectic manifolds , J. Geom. Anal. 18
2008
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S. K. Donaldson, Some numerical results in complex differential geometry , Pure Appl. Math. Q. 5
2009
Later among the works it cites.
M. R. Douglas and S. Klevtsov, Bergman kernel from path integral , Comm. Math. Phys. 293
2010
Closest in time.
J. Fine, Calabi flow and projective embeddings , with an Appendix by K. Liu and X. Ma, J. Differential Geom. 84
2010
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X. Ma, Geometric quantization on Kähler and symplectic manifolds , Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19–27, 2010. Vol II, 785–810
2010
Closest in time.