Randomly perturbed ergodic averages

We consider a class of random ergodic averages, containing averages along random non–integer sequences. For such averages, Cohen & Cuny obtained uniform universal pointwise convergence for functions in L^2 with \int \max (1,\log (1+|t|)) d\mu _f<\infty via a uniform estimation of trigonometri...

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Bibliographic Details
Published inProceedings of the American Mathematical Society. Series B Vol. 8; no. 19; pp. 224 - 244
Main Authors JaeYong Choi, Karin Reinhold-Larsson
Format Journal Article
LanguageEnglish
Published 02.07.2021
Subjects
universal convergence
Random ergodic averages
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Summary:We consider a class of random ergodic averages, containing averages along random non–integer sequences. For such averages, Cohen & Cuny obtained uniform universal pointwise convergence for functions in L^2 with \int \max (1,\log (1+|t|)) d\mu _f<\infty via a uniform estimation of trigonometric polynomials. We extend this result to L^2 functions satisfying the weaker condition \int \max (1,\log \log (1+|t|)) d\mu _f<\infty. We also prove that uniform universal pointwise convergence in L^2 holds for the corresponding smoothed random averages or for random averages whose kernels exhibit sufficient decay at infinity.
ISSN:2330-1511
2330-1511
DOI:10.1090/bproc/61