2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100190This paper is devoted to semi-classical aspects of symplectic reduction. Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus action. Guillemin and Sternberg introduced an isomorphism between the invariant part of the quantum space associated to M and the quantum space associated to the symplectic quotient of M, provided this quotient is non-singular. We prove that this isomorphism is a Fourier integral operator and that the Toeplitz operators of M descend to Toeplitz operators of the reduced phase space. We also extend these results to the case where the symplectic quotient is an orbifold and estimate the spectral density of a reduced Toeplitz operator, a result related to the Riemann-Roch-Kawazaki theorem.corrected typos, accepted for publication in J. Funct. AnalSymplectic GeometrySpectral Theory53D20; 53D50; 81S30; 47L80; 37P20text