Quantum Harmonic Analysis for Polyanalytic Fock Spaces
- authored by
- Robert Fulsche, Raffael Hagger
- Abstract
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 recent work by the second author 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.
- Organisation(s)
-
Institute of Analysis
- External Organisation(s)
-
Kiel University
- Type
- Article
- Journal
- Journal of Fourier Analysis and Applications
- Volume
- 30
- ISSN
- 1069-5869
- Publication date
- 01.11.2024
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Analysis, General Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.1007/s00041-024-10124-9 (Access:
Open)
