一维薛定谔算子谱位移函数的Weak Convergence
Weak Convergence of Spectral Shift Functions for One-Dimensional Schrödinger Operators
摘要：
研究了有限区间$(0,R)$上自伴一维薛定谔算子的谱移函数在无限体积极限$R\to\infty$内收敛到半线谱移函数的方式.借助弗雷德霍姆行列式方法，结合一定的测度论事实，证明了文献中Dirichlet边界条件的特殊情形下的先验淡收敛结果推广到弱收敛和任意分离自伴边界条件的概念，即在$x=0$和$x=R$ .
英文摘要：
We study the manner in which spectral shift functions associated with self-adjoint one-dimensional Schrödinger operators on the finite interval $(0,R)$ converge in the infinite volume limit $R\to\infty$ to the half-line spectral shift function. Relying on a Fredholm determinant approach combined with certain measure theoretic facts, we show that prior vague convergence results in the literature in the special case of Dirichlet boundary conditions extend to the notion of weak convergence and arbitrary separated self-adjoint boundary conditions at $x=0$ and $x=R$.
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