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

Leonid Golinskii; Stanislas Kupin; Juliette Leblond; Masimba Nemaire

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arXiv · 2204.12888

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

Leonid Golinskii·Stanislas Kupin·Juliette Leblond·Masimba Nemaire

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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.

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Leonid Golinskii, Stanislas Kupin, Juliette Leblond, Masimba Nemaire. 2022-04-27. On discrete spectra of Bergman--Toeplitz operators with harmonic symbols. https://arxiv.org/abs/2204.12888

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