Trace class Toeplitz operators with singular symbols

TL;DR

This paper characterizes when Toeplitz operators with distributional symbols are trace class on the Bergman space, introducing a Berezin transform for distributions and providing a trace formula with illustrative examples.

Contribution

It introduces a new characterization for trace class Toeplitz operators with distributional symbols and defines a Berezin transform for distributions.

Findings

Characterization of trace class membership for Toeplitz operators with distributional symbols

A formula for the trace involving the Berezin transform of distributions

Several examples illustrating the theory

Abstract

We characterize the trace class membership of Toeplitz operators with distributional symbols acting on the Bergman space on the unit disk. The Berezin transform of distributions, introduced in the paper, yields a formula for the trace. Several instructive examples are also given.