If the Vlasov-Poisson or Einstein-Vlasov system is linearized about an isotropic steady state, a linear operator arises the properties of which are relevant in the linear as well as nonlinear stability analysis of the given steady state. We prove that when defined on a suitable Hilbert space and equipped with the proper domain of definition this transport operator $ {\mathcal T} $ is skew-adjoint, i.e., $ {\mathcal T}^\ast = - {\mathcal T} $. In the Vlasov-Poisson case we also determine the kernel of this operator.

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关于关于各向同性稳态线性化Vlasov-Poisson或Einstein-Vlasov系统的运输算子

如果将Vlasov-Poisson或Einstein-Vlasov系统围绕各向同性稳态进行线性化，则会出现线性算子，其性质与给定稳态的线性和非线性稳定性分析相关。我们证明，当在合适的希尔伯特空间上定义并配备适当的定义域时，该运输算子$ {\ mathcal T} $是倾斜伴随的，即$ {\ mathcal T} ^ \ ast =-{\ mathcal T } $。在Vlasov-Poisson情况下，我们还确定了该运算符的内核。