PreprintCC0arXiv
Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space
Abstract
By constructing an appropriate quadratic form, we prove that if an analytic Toeplitz operator commutes with a co-analytic Toeplitz operator on the harmonic Bergman space, then at least one of the symbols is constant. This resolves an open question posed by Choe and Lee in 1999.
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BibTeX
@misc{tian2026commuting,
title = {{Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space}},
author = {Xianchi Tian and Jiawei Wang and Xianfeng Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14635},
eprint = {2609.14635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14635},
note = {CC0},
}
RIS
TY - UNPB
TI - Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space
AU - Xianchi Tian
AU - Jiawei Wang
AU - Xianfeng Zhao
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.14635
UR - https://arxiv.org/abs/2609.14635
AB - By constructing an appropriate quadratic form, we prove that if an analytic Toeplitz operator commutes with a co-analytic Toeplitz operator on the harmonic Bergman space, then at least one of the symbols is constant. This resolves an open question posed by Choe and Lee in 1999.
ER -