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arXiv · 2610.30209

Finite zero products of Toeplitz operators with harmonic symbols

Youqi Liu·Jie Qin·Sui Huang
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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.

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Youqi Liu, Jie Qin, Sui Huang. 2026-10-21. Finite zero products of Toeplitz operators with harmonic symbols. https://arxiv.org/abs/2610.30209

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