On discrete spectra of Bergman--Toeplitz operators with harmonic symbols

TL;DR

This paper investigates the distribution of discrete spectra of harmonic-symbol Toeplitz operators on Bergman spaces, applying classical perturbation theory and recent spectral distribution results to derive quantitative insights.

Contribution

It introduces a new quantitative analysis of the discrete spectrum distribution for harmonic-symbol Toeplitz operators using advanced spectral theory methods.

Findings

Quantitative description of the discrete spectrum distribution

Application of classical perturbation theory to Toeplitz operators

Extension of recent spectral distribution results to harmonic symbols

Abstract

In the present article, we study the discrete spectrum of certain bounded Toeplitz operators with harmonic symbol on a Bergman space. Using the methods of classical perturbaton theory and recent results by Borichev-Golinskii-Kupin and Favorov-Golinskii, we obtain a quantitative result on the distribution of the discrete spectrum of the operator in the unbounded (outer) component of its Fredholm set.