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

2022/04/27 by Leonid Golinskiĭ, Stanislas Kupin, Golinskii, Leonid +5
Mathematics · #30H20 #47A55 #47B35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.12888

openalex publication_date 2022/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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