加性同调方程的多维解
A multidimensional solution to additive homological equations
摘要：
本文证明了对于有限维实赋范空间$V$，每个有界平均零函数$f\in L_\infty([0,1];V)$对于$[0,1]$的某个$g\in L_\infty([0,1];V)$和某个遍历可逆保测度变换$T$都可以写成$f = g\circ T - g$形式.此外，我们的方法允许我们选择$g$，对于任何给定的$\varepsilon>0$，使得$\|g\|_\infty\leq (S_V+\varepsilon)\|f\|_\infty$，其中$S_V$是对应于$V$的Steinitz常数。
英文摘要：
In this paper 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 $V$.
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