Mean ergodic theorems in L^r(μ) and H^r(\mathbb T), 0

2023/12/31 by El Houcein El Abdalaoui, Michael Lin, Abdalaoui, el Houcein el +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Mathematical Dynamics and Fractals #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2401.00567

Abstract

Let T be the Koopman operator of a measure preserving transformation θ of a probability space (X,Σ,μ). We study the convergence properties of the averages M_nf:=\frac1n∑_k=0^n-1T^kf when f ∈ L^r(μ), 0

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