PreprintarXiv licencearXiv
The spectral structure of Toeplitz operators with polynomial symbols on the harmonic Bergman space
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)2n−1 isolated eigenvalues, where n is the degree of the symbol. This implies that Weyl's theorem holds for such operators.
Related
- Commuting Toeplitz operators with harmonic symbols on the Fock space
- Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space
- Zero products of Toeplitz operators with harmonic symbols on the Bergman space of the unit ball
- Finite zero products of Toeplitz operators with harmonic symbols
- Hypercyclic Bergman-Toeplitz operators with some harmonic symbols
BibTeX
@misc{huang2026spectral,
title = {{The spectral structure of Toeplitz operators with polynomial symbols on the harmonic Bergman space}},
author = {Mingmei Huang and Jiawei Wang and Xianfeng Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09638},
eprint = {2610.09638},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09638},
}
RIS
TY - UNPB
TI - The spectral structure of Toeplitz operators with polynomial symbols on the harmonic Bergman space
AU - Mingmei Huang
AU - Jiawei Wang
AU - Xianfeng Zhao
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09638
UR - https://arxiv.org/abs/2610.09638
AB - 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.
ER -