A Fourier Criterion for Recognizing Toeplitz Operators on Fock Spaces

Zhaopeng Lin; Yufeng Lu; Chao Zu

A Fourier Criterion for Recognizing Toeplitz Operators on Fock Spaces

Functional Analysis 2026-07-05 v1

Authors: Zhaopeng Lin , Yufeng Lu , Chao Zu

Abstract

We give a Fourier criterion for recognizing those bounded operators on Fock spaces that are Toeplitz operators with bounded measurable symbols. For a Toeplitz operator, the anti-diagonal restriction of its canonical kernel is the Fourier transform of the Gaussian-weighted symbol. Consequently, Fourier inversion of this anti-diagonal restriction recovers the unique bounded symbol whenever such a representation exists. As applications, we characterize bounded-symbol Toeplitz representability for weighted composition operators and generalized Volterra-type operators.

Keywords

Toeplitz operators Fock spaces Fourier criterion bounded symbols weighted composition operators Volterra-type operators

Cite

@article{arxiv.2607.04102,
  title  = {A Fourier Criterion for Recognizing Toeplitz Operators on Fock Spaces},
  author = {Zhaopeng Lin and Yufeng Lu and Chao Zu},
  journal= {arXiv preprint arXiv:2607.04102},
  year   = {2026}
}

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19 pages