The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator-valued Titchmarsh–Weyl m-function. This general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries and Schrödinger operators with compactly supported potentials. In these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps.

中文翻译：

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谱位移函数和 Dirichlet-to-Neumann 映射

一对自伴随算子的谱位移函数通过抽象算子值 Titchmarsh-Weyl m 函数表示。这个一般结果适用于具有紧凑边界的光滑域上的二阶椭圆偏微分算子和具有紧凑支持势的薛定谔算子的不同自伴随实现。在这些应用中，借助（依赖于能量参数的）狄利克雷-诺依曼映射，以显式形式确定谱位移函数。