Finite zero products of Toeplitz operators with harmonic symbols

@misc{liu2026finite,
  title = {{Finite zero products of Toeplitz operators with harmonic symbols}},
  author = {Youqi Liu and Jie Qin and Sui Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30209},
  eprint = {2610.30209},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30209},
}

TY  - UNPB
TI  - Finite zero products of Toeplitz operators with harmonic symbols
AU  - Youqi Liu
AU  - Jie Qin
AU  - Sui Huang
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30209
UR  - https://arxiv.org/abs/2610.30209
AB  - We study finite products of Toeplitz operators with harmonic symbols on the Fock space over the complex plane. If every symbol has the form f+g̅, where f and g are entire functions of exponential type, we prove that a finite product vanishes if and only if one symbol vanishes identically. It suffices to test the product on reproducing kernels. The proof represents the product by a two-variable entire function and transforms the equation for a left factor by exp(−∂_z∂_w). A Fock norm identity then permits cancellation of each nonzero factor.
ER  -