PreprintCC BY 4.0arXiv
Quantum harmonic analysis and the Differential operators on weighted Bergman spaces of bounded symmetric domains
Abstract
We develop quantum harmonic analysis (QHA) for operators on the parametrized Bergman space 𝒜2ν(Ω) of a bounded symmetric domain Ω, extending the theory previously known for the unit ball. Building on this framework, we introduce a class of differential operators acting on operators on 𝒜2ν(Ω). Combining these tools, we advance the theory of Toeplitz operators on 𝒜2ν(Ω): we establish Toeplitz approximation results via the α-Berezin transform, construct a differential operator Dα that shifts the α-Berezin transform, and obtain several characterizations of the radial Toeplitz algebra -- including one via the uniformly continuous radial operators, and one via the domain of Dα.
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BibTeX
@misc{dawson2026quantum,
title = {{Quantum harmonic analysis and the Differential operators on weighted Bergman spaces of bounded symmetric domains}},
author = {Matthew Dawson and Vishwa Dewage and Gestur Olafsson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33428},
eprint = {2610.33428},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33428},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum harmonic analysis and the Differential operators on weighted Bergman spaces of bounded symmetric domains
AU - Matthew Dawson
AU - Vishwa Dewage
AU - Gestur Olafsson
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33428
UR - https://arxiv.org/abs/2610.33428
AB - We develop quantum harmonic analysis (QHA) for operators on the parametrized Bergman space 𝒜^2_ν(Ω) of a bounded symmetric domain Ω, extending the theory previously known for the unit ball. Building on this framework, we introduce a class of differential operators acting on operators on 𝒜^2_ν(Ω). Combining these tools, we advance the theory of Toeplitz operators on 𝒜^2_ν(Ω): we establish Toeplitz approximation results via the α-Berezin transform, construct a differential operator D_α that shifts the α-Berezin transform, and obtain several characterizations of the radial Toeplitz algebra -- including one via the uniformly continuous radial operators, and one via the domain of D_α.
ER -