Almost everywhere convergence of convolution powers without finite second moment

2010/08/07 by Christopher M. Wedrychowicz, Wedrychowicz, Christopher M. · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #math.CA

paper · pdf · doi:10.48550/arxiv.1008.1329

13 pages, to appear in Annales de l Institut Fourier

arxiv created 2010/08/07 · openalex publication_date 2010/08/07 · arxiv updated 2010/08/10 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We generalize a theorem of Bellow and Calderón concerning the a.e. convergence of the convolution powers \ds μⁿf(x)=∑_kμⁿ(k)f(T^k x) where T is a measure preserving transformation of a probability space and μ is a probability measure on the integers.

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