Uniform convergence in von Neumann's ergodic theorem in the absence of a\n spectral gap

2019/02/11 by Jonathan Ben‐Artzi, Ben-Artzi, Jonathan, Baptiste Morisse +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1902.03953

openalex publication_date 2019/02/11 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

Von Neumann's original proof of the ergodic theorem is revisited. A uniform\nconvergence rate is established under the assumption that one can control the\ndensity of the spectrum of the underlying self-adjoint operator when restricted\nto suitable subspaces. Explicit rates are obtained when the bound is\npolynomial, with applications to the linear Schr "odinger and wave equations.\nIn particular, decay estimates for time-averages of solutions are shown.\n

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