论文标题
加权千古平均值的收敛性
Convergence of weighted ergodic averages
论文作者
论文摘要
令$（X，\ Mathcal {a}，μ）$为概率空间，让$ t $成为$ l^2（μ）$的收缩。我们以序列$（w_k）$，$（u_k）$和$（a_k）$的方式提供适当的条件，以使加权的Ergodic限制$ \ lim \ lim \ limits_ {n \ rightarrow \ rightArrow \ infty} \ frac {1} $μ$ -A.E。对于任何功能，$ f $ in $ l^2（μ）$。由于我们的主要定理，我们还处理了所谓的单侧加权的嗜好希尔伯特变革。
Let $(X, \mathcal{A},μ)$ be a probability space and let $T$ be a contraction on $L^2(μ)$. We provide suitable conditions over sequences $(w_k)$, $(u_k)$ and $(A_k)$ in such a way that the weighted ergodic limit $\lim\limits_{N\rightarrow\infty}\frac{1}{A_N}\sum_{k=0}^{N-1} w_k T^{u_k}(f)=0$ $μ$-a.e. for any function $f$ in $L^2(μ)$. As a consequence of our main theorems, we also deal with the so-called one-sided weighted ergodic Hilbert transforms.
