2023/08/22 by Robert Fulsche, Fulsche, Robert, Raffael Hagger +1 · 1 citation
Mathematics · #30H20 #47B07 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 47L80 #Secondary: 47B35
paper · pdf · doi:10.48550/arxiv.2308.11292
openalex publication_date 2023/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in arXiv:2201.10230 and answer a few related open questions. For instance, we show that there exists a symbol such that the corresponding Toeplitz operator is unitary on the analytic Fock space but vanishes completely on one of the true polyanalytic Fock spaces. This follows directly from an explicit characterization of the kernel of the Toeplitz quantization, which we derive using quantum harmonic analysis. Moreover, we show that the Berezin transform is injective on the set of of Toeplitz operators. Finally, we provide several characterizations of the C1-algebra in terms of integral kernel estimates and essential commutants.