3 research outputs found
A multidimensional solution to additive homological equations
In this paper we prove that for a finite-dimensional real normed space , every bounded mean zero function can be written in the form
for some and some ergodic invertible measure preserving transformation of .
Our method moreover allows us to choose , for any given , to be such that , where is the Steinitz constant corresponding to
A solution to the multidimensional additive homological equation
We prove that, for a finite-dimensional real normed space V, every bounded mean zero function f β Lβ([0, 1]; V) can be written in the form f = g β¦ T β g for some g β Lβ([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 Ξ΅ > 0, to be such that β₯gβ₯β β©½ (SV + Ξ΅)β₯fβ₯β, where SV is the Steinitz constant corresponding to V
A multidimensional solution to additive homological equations
In this paper we prove that for a finite-dimensional real normed space , every bounded mean zero function can be written in the form
for some and some ergodic invertible measure preserving transformation of .
Our method moreover allows us to choose , for any given , to be such that , where is the Steinitz constant corresponding to