Details
| Original language | English |
|---|---|
| Article number | 63 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 30 |
| Issue number | 6 |
| Publication status | Published - 1 Nov 2024 |
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.
Keywords
- Polyanalytic Fock space, Quantum harmonic analysis, Reproducing kernels, Toeplitz algebra, Toeplitz operators
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Mathematics(all)
- Applied Mathematics
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In: Journal of Fourier Analysis and Applications, Vol. 30, No. 6, 63, 01.11.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum Harmonic Analysis for Polyanalytic Fock Spaces
AU - Fulsche, Robert
AU - Hagger, Raffael
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/11/1
Y1 - 2024/11/1
N2 - 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.
AB - 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.
KW - Polyanalytic Fock space
KW - Quantum harmonic analysis
KW - Reproducing kernels
KW - Toeplitz algebra
KW - Toeplitz operators
UR - http://www.scopus.com/inward/record.url?scp=85208587594&partnerID=8YFLogxK
U2 - 10.1007/s00041-024-10124-9
DO - 10.1007/s00041-024-10124-9
M3 - Article
AN - SCOPUS:85208587594
VL - 30
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
SN - 1069-5869
IS - 6
M1 - 63
ER -