A solution to the multidimensional additive homological equation
Алексей Феликсович БерNational University of Uzbekistan named after M. Ulugbek, TashkentMatthijs BorstDelft Institute of Applied Mathematics, Delft University of Technology, Delft, The NetherlandsSander BorstCentrum Wiskunde and Informatica, Amsterdam, The NetherlandsFedor SukochevSchool of Mathematics and Statistics, University of New South Wales,
Kensington, Australia
ABI
Annotatsiya
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 $V$.
Mavzular
Identifikatorlar
Iqtiboslar va manbalar
0 ta iqtibos21 ta foydalanilgan manba
Koʻrsatkichlar — AkademScholar · Tez orada