A solution to the multidimensional additive homological equation
- 作者: Ber A.F.1, Borst M.2, Borst S.3, Sukochev F.A.4
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隶属关系:
- National University of Uzbekistan named after M. Ulugbek, Faculty of Mathematics and Mechanics
- Delft University of Technology
- Centrum voor Wiskunde en Informatica
- University of New South Wales, School of Mathematics and Statistics
- 期: 卷 87, 编号 2 (2023)
- 页面: 3-55
- 栏目: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/133896
- DOI: https://doi.org/10.4213/im9319
- ID: 133896
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详细
We prove that, for a finite-dimensional real normed space $V$,every bounded mean zero function $f\in L_\infty([0,1];V)$can be written in the form $f=g\circ T-g$ for some $g\in L_\infty([0,1];V)$and some ergodic invertible measure preserving transformation $T$of $[0,1]$.Our method moreover allows us to choose $g$, for any given $\varepsilon>0$,to be such that $\|g\|_\infty\leq (S_V+\varepsilon)\|f\|_\infty$,where $S_V$ is the Steinitz constant corresponding to $V$.
作者简介
Aleksei Ber
National University of Uzbekistan named after M. Ulugbek, Faculty of Mathematics and Mechanics
Email: ber@ucd.uz
Candidate of physico-mathematical sciences, Senior Researcher
Matthijs Borst
Delft University of Technology
Email: m.j.borst@outlook.com
Sander Borst
Centrum voor Wiskunde en Informatica
Email: sander.borst@cwi.nl
Fedor Sukochev
University of New South Wales, School of Mathematics and Statistics
Email: f.sukochev@unsw.edu.au
Candidate of physico-mathematical sciences, Professor
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