Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2018_30_2_a7,
author = {Yu. A. Kordyukov},
title = {On asymptotic expansions of generalized {Bergman} kernels on symplectic manifolds},
journal = {Algebra i analiz},
pages = {163--187},
publisher = {mathdoc},
volume = {30},
number = {2},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AA_2018_30_2_a7/}
}
Yu. A. Kordyukov. On asymptotic expansions of generalized Bergman kernels on symplectic manifolds. Algebra i analiz, Tome 30 (2018) no. 2, pp. 163-187. http://geodesic.mathdoc.fr/item/AA_2018_30_2_a7/
[1] Meladze G. A., Shubin M. A., “Sobstvennye ravnomernye psevdodifferentsialnye operatory na unimodulyarnykh gruppakh Li”, Tr. semin. im. I. G. Petrovskogo, 11, 1986, 74–97
[2] Meladze G. A., Shubin M. A., “Funktsionalnoe ischislenie psevdodifferentsialnykh operatorov na unimodulyarnykh gruppakh Li”, Tr. semin. im. I. G. Petrovskogo, 12, 1987, 164–200
[3] Bismut J.-M., Vasserot E., “The asymptotics of the Ray–Singer analytic torsion associated with high powers of a positive line bundle”, Comm. Math. Phys., 125 (1989), 355–367 | DOI | MR
[4] Borthwick D., Uribe A., “Almost complex structures and geometric quantization”, Math. Res. Lett., 3 (1996), 845–861 | DOI | MR
[5] Braverman M., “Vanishing theorems on covering manifolds”, Tel Aviv Topology Conference, Rothenberg Festschrift (1998), Contemp. Math., 231, Amer. Math. Soc., Providence, RI, 1999, 1–23 | DOI | MR
[6] Dai X., Liu K., Ma X., “On the asymptotic expansion of Bergman kernel”, J. Differential Geom., 72:1 (2006), 1–41 | DOI | MR
[7] Guillemin V., Uribe A., “The Laplace operator on the $n$th tensor power of a line bundle: eigenvalues which are uniformly bounded in $n$”, Asymptotic Anal., 1:2 (1988), 105–113 | MR
[8] Ioos L., Lu W., Ma X., Marinescu G., Berezin–Toeplitz quantization for eigenstates of the Bochner-Laplacian on symplectic manifolds, Preprint, arXiv: 1703.06420
[9] Kordyukov Yu. A., “$L^p$-theory of elliptic differential operators on manifolds of bounded geometry”, Acta Appl. Math., 23:3 (1991), 223–260 | MR
[10] Kordyukov Yu. A., “$L^p$-estimates for functions of elliptic operators on manifolds of bounded geometry”, Russ. J. Math. Phys., 7:2 (2000), 216–229 | MR
[11] Lu W., Ma X., Marinescu G., “Donaldson's Q-operators for symplectic manifolds”, Sci. China Math., 60:6 (2017), 1047–1056 | DOI | MR
[12] Ma X., Marinescu G., “The $Spin^c$ Dirac operator on high tensor powers of a line bundle”, Math. Z., 240:3 (2002), 651–664 | DOI | MR
[13] Ma X., Marinescu G., Holomorphic Morse inequalities and Bergman kernels, Progr. Math., 254, Birkhäuser Verlag, Basel, 2007 | MR
[14] Ma X., Marinescu G., “Generalized Bergman kernels on symplectic manifolds”, Adv. Math., 217:4 (2008), 1756–1815 | DOI | MR
[15] Ma X., Marinescu G., “Toeplitz operators on symplectic manifolds”, J. Geom. Anal., 18:2 (2008), 565–611 | DOI | MR