On kernels of Toeplitz operators

Toeplitz Operators and Weighted Bergman Kernels

For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman...

Szegö Kernels, Toeplitz Operators, and Equivariant Fixed Point Formulae

The aim of this paper is to apply algebro-geometric Szegö kernels to the asymptotic study of a class of trace formulae in equivariant geometric quantization and algebraic geometry. Let (M,J) be a connected complex projective manifold, of complex dimension d, and let A be an ample line bundle on it. Let, in addition, G be a compact and connected g-dimensional Lie group acting holomorphically on ...

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...

Toeplitz Operators on Fock Spaces

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...