Details
Originalsprache | Englisch |
---|---|
Aufsatznummer | 109778 |
Fachzeitschrift | Journal of Functional Analysis |
Jahrgang | 284 |
Ausgabenummer | 4 |
Frühes Online-Datum | 23 Nov. 2022 |
Publikationsstatus | Veröffentlicht - 15 Feb. 2023 |
Abstract
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
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in: Journal of Functional Analysis, Jahrgang 284, Nr. 4, 109778, 15.02.2023.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Self-adjointness of Toeplitz operators on the Segal-Bargmann space
AU - Bauer, Wolfram
AU - van Luijk, Lauritz
AU - Stottmeister, Alexander
AU - Werner, Reinhard F.
N1 - Funding Information: We thank Robert Fulsche for helpful discussions and suggestions. The second named author acknowledges support by the Quantum Valley Lower Saxony.
PY - 2023/2/15
Y1 - 2023/2/15
N2 - We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of Hamiltonian functions for classical mechanics. For this we extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces. Finally, we apply our result to prove self-adjointness for a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schr\"odinger representation.
AB - We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of Hamiltonian functions for classical mechanics. For this we extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces. Finally, we apply our result to prove self-adjointness for a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schr\"odinger representation.
KW - Segal-Bargmann space
KW - Self-adjointness
KW - Toeplitz operator
KW - Unbounded
UR - http://www.scopus.com/inward/record.url?scp=85143700075&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2202.04687
DO - 10.48550/arXiv.2202.04687
M3 - Article
VL - 284
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 4
M1 - 109778
ER -