AI 中文总结
研究全直线遍历块雅可比算子的终极石井 - 帕斯特定理，通过证明最大谱测度在特定区域的限制由零容量博雷尔集承载，在标量情形下解决了相关全直线问题。
AI 中文摘要
我们建立了全直线遍历块雅可比算子的终极石井 - 帕斯特定理。证明了对于几乎每个实现，最大谱测度在最小非负李雅普诺夫指数严格为正的区域上的限制由零容量的博雷尔集承载。在标量情况下，解决了达马尼和菲尔曼提出的全直线问题。
英文摘要
We establish an ultimate Ishii-Pastur theorem for whole-line ergodic block Jacobi operators. We prove that, for almost every realization, the restriction of a maximal spectral measure to the region where the smallest nonnegative Lyapunov exponent is strictly positive is carried by a Borel set of zero capacity. In the scalar case, this settles the whole-line problem formulated by Damanik and Fillman \cite[Problem~4.7.18]{Damanik-Fillman-book}.
