Familles d'opérateurs de Toeplitz, indice des familles et quantification par déformations
Abstract
Given a contact fibration, we construct smooth families of Szegö projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these operators to construct a deformation quantization of prequantizable symplectic fibrations, recovering a result of Kravchenko in an analytic way. We also derive a family index for these families of Toeplitz operators. To this end, we generalize an index formula of Baum and van Erp to families.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Operator Algebra Research
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- HAL (Le Centre pour la Communication Scientifique Directe)
- Publication date
- 11 January 2026
- Language
- EN
- Document type
- Preprint