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 -