Randomly perturbed ergodic averages
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- by JaeYong Choi and Karin Reinhold-Larsson;
- Proc. Amer. Math. Soc. Ser. B 8 (2021), 224-244
- DOI: https://doi.org/10.1090/bproc/61
- Published electronically: July 2, 2021
- HTML | PDF
Abstract:
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.References
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Bibliographic Information
- JaeYong Choi
- Affiliation: Division of Mathematics and Computer Science (DMACS), College of Natural and Applied Sciences (CNAS), University of Guam (UOG), ALS 319, UOG Station, Mangilao, 96923 Guam
- ORCID: 0000-0002-9912-0867
- Email: choij@triton.uog.edu
- Karin Reinhold-Larsson
- Affiliation: Department of Mathematics and Statistics, University at Albany, SUNY, Albany, New York 12222
- MR Author ID: 324489
- Email: reinhold@albany.edu
- Received by editor(s): October 10, 2018
- Received by editor(s) in revised form: August 31, 2020, and September 11, 2020
- Published electronically: July 2, 2021
- Communicated by: Nimish Shah
- © Copyright 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 224-244
- MSC (2020): Primary 37A05, 28D05
- DOI: https://doi.org/10.1090/bproc/61
- MathSciNet review: 4281342