关于Kotani-Last和Schrodinger猜想
On the Kotani-Last and Schrodinger conjectures
摘要：
在遍历一维Schrodinger算子理论中，ac谱一直被认为是严格的。在这个方向上的两个关键命题，一方面，交流频谱要求几乎周期性的潜力，另一方面，本征函数几乎必然有界的交流频谱的本质支持。我们展示了如何周期性势的反复缓慢变形可以用来打破刚性，并反驳了这两个命题。
英文摘要：
In the theory of ergodic one-dimensional Schrodinger operators, ac spectrum has been traditionally expected to be very rigid. Two key conjectures in this direction state, on one hand, that ac spectrum demands almost periodicity of the potential, and, on the other hand, that the eigenfunctions are almost surely bounded in the essential suport of the ac spectrum. We show how the repeated slow deformation of periodic potentials can be used to break rigidity, and disprove both conjectures.
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