紧区间上Schrodinger算子的边界数据映射
Boundary Data Maps for Schrodinger Operators on a Compact Interval
摘要：
本文系统地研究了边界数据映射，即2 \times 2矩阵值Dirichlet-to-Neumann映射和更一般的Robin-to-Robin映射，它们与紧区间[0，R]上的一维Schrodinger算子相关联，在0和R处具有分离的边界条件.我们的大部分结果是在非自伴的情况下得到的。我们的主要结果包括这些边界数据映射的显式表示的基础薛定谔算子的预解式和相关的边界迹映射，Krein型预解式公式有关薛定谔算子对应于不同的（分离）边界条件，以及边界数据映射的Herglotz性质的推导（直到右乘适当的对角矩阵）。
英文摘要：
We provide a systematic study of boundary data maps, that is, 2 \times 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrodinger operators on a compact interval [0,R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent of the underlying Schrodinger operator and the associated boundary trace maps, Krein-type resolvent formulas relating Schrodinger operators corresponding to different (separated) boundary conditions, and a derivation of the Herglotz property of boundary data maps (up to right multiplication by an appropriate diagonal matrix) in the special self-adjoint case.
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