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The Brown-Halmos theorems on the Fock space
- Publication Year :
- 2023
-
Abstract
- In this paper, we extend the Brown-Halmos theorems to the Fock space and investigate the range of the Berezin transform. We observe that there are non-pluriharmonic functions $u$ that can be written as a finite sum $B(u)=\sum_lf_l\overline{g_l}$, where $f_l,g_l$ are holomorphic functions belonging to the class $\mathrm{Sym}(\mathbb{C}^n)$. In addition, we solve an open question about the zero product of Toeplitz operators, which was posed by Bauer et al. in 2015. Our results reveal that the Brown-Halmos theorems on the Fock space are more complicated than that on the classical Bergman space.<br />Comment: 19 pages
- Subjects :
- Mathematics - Complex Variables
Mathematics - Functional Analysis
30H20, 47B35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.16613
- Document Type :
- Working Paper