We develop the quantum harmonic analysis framework in the reducible setting and apply
our findings to polyanalytic Fock spaces. In particular, we explain some phenomena …

Given φ ∈\verb" C"^ 2 (C^ n) φ∈ C 2 (C n) satisfying dd^ c φ ≃\omega_0 ddc φ≃ ω 0, 0<
p<∞, let F^ p (φ) F p (φ) be the generalized Fock space of all holomorphic functions f …

The purpose of this paper is twofold. We first establish a sharp version of Forelli–Rudin
estimates for certain integrals on the ball. Then, as main application of these estimates, we …

Let T f denote the Toeplitz operator with symbol function f on the Bergman space L a 2 (B,
dv) of the unit ball in C n. It is a natural problem in the theory of Toeplitz operators to …

We generalize several results on Toeplitz operators over reflexive, standard weighted Fock
spaces F pt to the non-reflexive cases p D 1; 1. Among these results are the characterization …

We discuss the compactness of Hankel operators on Hardy, Bergman and Fock spaces with
focus on the differences between the three cases, and complete the theory of compact …

We use results and techniques from Werner's``quantum harmonic analysis''to show that $ G
$-invariant Toeplitz operators are norm dense in $ G $-invariant Toeplitz algebras for all …

In this paper, we introduce techniques from complex harmonic analysis to prove a weaker
version of the Geometric Arveson-Douglas Conjecture on the Bergman space for a complex …

We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz
operators and extend one part of this theorem to the setting of p-Fock spaces (1≤ p≤∞) …

We introduce an algebra $\mathcal W_t $ of linear operators that act continuously on each of
the Fock spaces $ F_t^ p $, $1\leq p\leq\infty $, and contains all Toeplitz operators with …