Toeplitz Operators on Symplectic Manifolds

Toeplitz Operators on Symplectic Manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established. 0. Introduction Quant...

Cohomologies and Elliptic Operators on Symplectic Manifolds

In joint work with S.-T. Yau, we construct new cohomologies of differential forms and elliptic operators on symplectic manifolds. Their construction can be described simply following a symplectic decomposition of the exterior derivative operator into two first-order differential operators, which are analogous to the Dolbeault operators in complex geometry. These first-order operators lead to ne...

On Weighted Toeplitz Operators

A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...

Relation of the Spectra of Symplectic Rarita-schwinger and Dirac Operators on Flat Symplectic Manifolds

Consider a flat symplectic manifold (M, ω), l ≥ 2, admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If λ is an eigenvalue of the symplectic Dirac operator such that −ılλ is not a symplectic Killing numbe...

Toeplitz Operators on Fock Spaces