Quasimodes and Bohr-Sommerfeld conditions for the Toeplitz operators. (English) Zbl 1038.53086
Let \((M,\omega)\) be a compact symplectic manifold. In the paper under review the author gives a quantization of the Lagrangian submanifolds of \(M\) by generalizing the ansatz for the Schwartz kernel of a Toeplitz operator. Then he applies this to produce the quasimodes of Toeplitz operators and to obtain the Bohr-Sommerfeld conditions.
Reviewer: Mircea Puta (Timişoara)
MSC:
| 53D50 | Geometric quantization |
| 53D12 | Lagrangian submanifolds; Maslov index |
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
| 81S10 | Geometry and quantization, symplectic methods |
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