The spectral structure of Toeplitz operators with polynomial symbols on the harmonic Bergman space
Year: 2026
Type: preprint
Abstract: Using the theory of symmetric polynomials, we prove that the spectrum of every Toeplitz operator with an analytic polynomial symbol on the harmonic Bergman space can be represented as the union of a closed curve and a finite set of at most $(n-1)2^{n-1}$ isolated eigenvalues, where $n$ is the degree of the symbol. This implies that Weyl's theorem holds for such operators.
Source: arXiv (Cornell University)
Authors: Huang, Mingmei, Wang, Jiawei, Zhao, Xianfeng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5351725556
OpenAlex ID: W7220922834