Details
| Original language | English |
|---|---|
| Article number | 38 |
| Journal | Journal of Pseudo-Differential Operators and Applications |
| Volume | 16 |
| Issue number | 2 |
| Early online date | 23 May 2025 |
| Publication status | Published - Jun 2025 |
Abstract
We prove a new criterion for essential self-adjointness of pseudodifferential operators, which does not involve ellipticity-type assumptions. Essential self-adjointness is proved for symbols in C2d+3 with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on L2(Rd), Calderón-Vaillancourt type theorems and a recent self-adjointness result for Toeplitz operators.
Keywords
- Operator-valued symbols, Pseudodifferential operators, Self-adjointness, Weyl quantization
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Pseudo-Differential Operators and Applications, Vol. 16, No. 2, 38, 06.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A simple criterion for essential self-adjointness of Weyl pseudodifferential operators
AU - Fulsche, Robert
AU - van Luijk, Lauritz
N1 - Publisher Copyright: © The Author(s) 2025.
PY - 2025/6
Y1 - 2025/6
N2 - We prove a new criterion for essential self-adjointness of pseudodifferential operators, which does not involve ellipticity-type assumptions. Essential self-adjointness is proved for symbols in C2d+3 with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on L2(Rd), Calderón-Vaillancourt type theorems and a recent self-adjointness result for Toeplitz operators.
AB - We prove a new criterion for essential self-adjointness of pseudodifferential operators, which does not involve ellipticity-type assumptions. Essential self-adjointness is proved for symbols in C2d+3 with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on L2(Rd), Calderón-Vaillancourt type theorems and a recent self-adjointness result for Toeplitz operators.
KW - Operator-valued symbols
KW - Pseudodifferential operators
KW - Self-adjointness
KW - Weyl quantization
UR - http://www.scopus.com/inward/record.url?scp=105005785656&partnerID=8YFLogxK
U2 - 10.1007/s11868-025-00699-2
DO - 10.1007/s11868-025-00699-2
M3 - Article
VL - 16
JO - Journal of Pseudo-Differential Operators and Applications
JF - Journal of Pseudo-Differential Operators and Applications
SN - 1662-9981
IS - 2
M1 - 38
ER -