Year: 2026
Type: preprint
Abstract: We answer Bauer and Le's question on zero products of Toeplitz operators on the Fock space $F^2(\mathbb C^n)$[JFA, 261 (2011), 9, 2617--2640]. For $n\ge2$, we construct two bounded nonradial Schwartz symbols on $\mathbb C^n$ whose Toeplitz operators are nonzero and have zero product on $F^2(\mathbb C^n)$. For $n=1$ and each $c\in(1/2,1)$, we construct two smooth nonradial symbols of growth at most $Ce^{c|z|^2}$ for some constant $C>0$. Their extended Toeplitz operators in $F^2(\mathbb C)$ are nonzero and have zero product on all holomorphic polynomials. Moreover, the second symbol is bounded when $c\geq3/4$. Our proofs use Gaussian kernel calculations, matrix identities, theta functions and Fourier transform.
Source: arXiv (Cornell University)
Author: Qin, Jie
Institution: Chongqing Technology and Business University
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G776706447
OpenAlex ID: W7213588291
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