带隙背景下Schroedinger算子的迹公式与散射理论
Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds
摘要：
本文利用Krein谱移理论研究了一维Schroedinger算子的迹公式，这类算子是拟周期有限间隙算子的迹族扰动。特别是，我们建立了这类Korteweg-de Vries族的解决方案的守恒量，并将它们与反射系数通过阿贝尔积分的基础超椭圆黎曼曲面。
英文摘要：
We investigate trace formulas for one-dimensional Schroedinger operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular, we establish the conserved quantities for the solutions of the Korteweg-de Vries hierarchy in this class and relate them to the reflection coefficients via Abelian integrals on the underlying hyperelliptic Riemann surface.
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