Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 2023 |
Abstract
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2023.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - A simple criterion for essential self-adjointness of Weyl pseudodifferential operators
AU - Fulsche, Robert
AU - van Luijk, Lauritz
PY - 2023
Y1 - 2023
N2 - We prove new criteria for essential self-adjointness of pseudodifferential operators which do not involve ellipticity type assumptions. For example, we show that self-adjointness holds in case that the symbol is $C^{2d+3}$ 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 $L^2(\mathbb{R}^d)$, Calderón-Vaillancourt type theorems and a recent self-adjointness result for Toeplitz operators on the Segal-Bargmann space developed in [1].
AB - We prove new criteria for essential self-adjointness of pseudodifferential operators which do not involve ellipticity type assumptions. For example, we show that self-adjointness holds in case that the symbol is $C^{2d+3}$ 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 $L^2(\mathbb{R}^d)$, Calderón-Vaillancourt type theorems and a recent self-adjointness result for Toeplitz operators on the Segal-Bargmann space developed in [1].
U2 - 10.48550/ARXIV.2304.07153
DO - 10.48550/ARXIV.2304.07153
M3 - Preprint
BT - A simple criterion for essential self-adjointness of Weyl pseudodifferential operators
ER -