微分算子的对称扩张及Friedrichs扩张的辛几何刻画

Complex Symplectic Geometry Characterizations for Symmetric Extensions and Priedrichs Extensions of Differential Operators

本文在加权Hilbert空间L2(I,r(x))(I=(a,6),-∞≤a<b≤∞,r(x)> 0)中,利用辛几何,刻画了n阶对称微分算式的最小算子的对称扩张(含自伴扩张)及 Friedrichs扩张,分别获得了其扩张为对称扩张、Friedrichs扩张的充分必要条件．

In this paper, we give complex symplectic geometry characterizations for symmetric extensions （including self-adjoint extensions） and Friedrichs extension of the minimal operator generated by nth-order symmetric differential expression, defined in the weighted Hilbert space L^2（I,r（x）） （the non-degenerate interval I, with endpoints -∞≤ a, b ≤ ∞）. The necessary and sufficient conditions which ensure that its extensions are symmetric extensions, Friedrichs extension are obtained respectively.