Details
| Original language | English |
|---|---|
| Article number | 109778 |
| Journal | Journal of Functional Analysis |
| Volume | 284 |
| Issue number | 4 |
| Early online date | 23 Nov 2022 |
| Publication status | Published - 15 Feb 2023 |
Abstract
Keywords
- Segal-Bargmann space, Self-adjointness, Toeplitz operator, Unbounded
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of Functional Analysis, Vol. 284, No. 4, 109778, 15.02.2023.
Research output: Contribution to journal › Article › Research › 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 -