论文标题
无反射的规范系统，ii。几乎是周期性和角色自动形态傅立叶变换
Reflectionless canonical systems, II. Almost periodicity and character-automorphic Fourier transforms
论文作者
论文摘要
我们开发了一种具有任意差异性规范频谱的无反射规范系统的综合理论，具有直接的cauchy定理属性。这将有限差距准二元（代数几何）解决方案的固定式集成层次结构的构造概括为无限的间隙设置。该结构不是在紧凑的Riemann表面上发挥作用，而是基于在Martin量的Widom域中繁殖了Widom域中的角色 - 型耐形空间的内核。我们还构建了统一的角色形状傅立叶变换，从而推广了佩奇定理。最后，我们发现了几乎周期性的正确概念，该概念适用于AROV仪表中的规范系统参数，并且我们证明，对于Potapov-de Branges Granges Granges Granges Granges和Dirac Operators几乎是最佳的结果。
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap quasiperiodic (algebro-geometric) solutions of stationary integrable hierarchies. Instead of theta functions on a compact Riemann surface, the construction is based on reproducing kernels of character-automorphic Hardy spaces in Widom domains with respect to Martin measure. We also construct unitary character-automorphic Fourier transforms which generalize the Paley-Wiener theorem. Finally, we find the correct notion of almost periodicity which holds for canonical system parameters in Arov gauge, and we prove generically optimal results for almost periodicity for Potapov-de Branges gauge, and Dirac operators.
