Year: 2026
Type: preprint
Abstract: We study finite products of Toeplitz operators with harmonic symbols on the Fock space over the complex plane. If every symbol has the form $f+\overline g$, 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 $\exp(-\partial_z\partial_w)$. A Fock norm identity then permits cancellation of each nonzero factor.
Source: arXiv (Cornell University)
Authors: Liu, Youqi, Qin, Jie, Huang, Sui
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223402733