In this paper we characterize the compact operators on the weighted Bergman spaces Ap α(Bn) when 1 <p< ∞ and α > −1. The main result shows that an operator on Ap α(Bn) is compact if and only if it belongs to the Toeplitz ...

We show that Levinson's basic principle for the solution of normal equations which are of Toeplitz form may he extended to the case where these equations do not possess this specific symmetry. The use of Levinson's principle ...

Let A2 be the Bergman space on the unit disk. A bounded operator S on A2 is called radial if Szn = λnzn for all n 0, where λn is a bounded sequence of complex numbers. We characterize the eigenvalues of radial operators ...

Let Ap be the Bergman space on the unit ball Bn of Cn for 1 <p< ∞, and Tp be the corresponding Toeplitz algebra. We show that every S ∈ Tp can be approximated by operators that are specially suited for the study of local ...

We define and study coherent states, a Berezin-Toeplitz quantization and covariant symbols on the product Xi := G x g(#) between a connected simply connected nilpotent Lie group and the dual of its Lie algebra. The starting ...