The spectral picture of Bergman-Toeplitz operators with harmonic polynomial symbols (Q6090792)

The authors state that for each integer \(k\ge 2\), there exists a polynomial \(P\) of degree \(k\) such that \(\sigma(T_{\overline{z}+P})\), the spectrum of the Toeplitz operator \(T_{\overline{z}+P}\) with the harmonic symbol \(\overline{z}+P\) has an isolated point (Theorem 4.1) and for a suitable class of polynomials \(P\), they state that \(\sigma(T_{\overline{z}+P})\) is a nonempty finite set (Theorem 4.3).