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Uniform convergence in von Neumann’s ergodic theorem in the absence of a spectral gap
Ergodic Theory and Dynamical Systems ( IF 0.9 ) Pub Date : 2020-04-13 , DOI: 10.1017/etds.2020.30
JONATHAN BEN-ARTZI , BAPTISTE MORISSE

Von Neumann’s original proof of the ergodic theorem is revisited. A uniform convergence rate is established under the assumption that one can control the density of the spectrum of the underlying self-adjoint operator when restricted to suitable subspaces. Explicit rates are obtained when the bound is polynomial, with applications to the linear Schrödinger and wave equations. In particular, decay estimates for time averages of solutions are shown.

中文翻译:

在没有谱隙的情况下冯诺依曼遍历定理的均匀收敛

冯诺依曼对遍历定理的原始证明被重新审视。一个统一的收敛速度是在一个假设下建立的,即当限制在合适的子空间时,可以控制底层自伴随算子的谱密度。当界限是多项式时,可以获得显式速率,并应用于线性薛定谔方程和波动方程。特别是,显示了解的时间平均值的衰减估计。
更新日期:2020-04-13
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