Quantum Harmonic Analysis on the Unweighted Bergman Space of the Unit Ball

Abstract

We study quantum harmonic analysis (QHA) on the Bergman space ${\mathcal{A}}^2({\mathbb{B}}^n)$ over the unit ball in ${\mathbb{C}}^n$. We formulate a Wiener's Tauberian theorem, and characterizations of the radial Toeplitz algebra over ${\mathcal{A}}^2({\mathbb{B}}^n)$. We discuss the $\alpha$-Berezin transform and investigate the question of approximations by Toeplitz operators.

44 pages