论文标题
电源有限的运算符和平均千古定理用于子序列
Power bounded operators and the mean ergodic theorem for subsequences
论文作者
论文摘要
让$ t $成为一个没有单模型特征值的电力界面的希尔伯特太空运营商。我们表明，随后的ergodic平均值$ n^{ - 1} \ sum_ {n = 1}^n t^{a_n} $在强序列$（a_n）$中收集在强操作员拓扑中，其中包括大多数层压型顽固性艰苦函数的整数部分。此外，我们表明加权平均值$ n^{ - 1} \ sum_ {n = 1}^n e^{2πig（n）} t^{a_n} $也收敛于许多合理的函数$ g $。特别是，由于Ter Elst和第二作者\ cite {tem}，我们将多项式均值定理推广为幂界算子，并将其概括为真实的多项式和多项式权重。
Let $T$ be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages $N^{-1}\sum_{n=1}^N T^{a_n}$ converge in the strong operator topology for a wide range of sequences $(a_n)$, including the integer part of most of subpolynomial Hardy functions. Moreover, we show that the weighted averages $N^{-1}\sum_{n=1}^N e^{2πi g(n)}T^{a_n}$ also converge for many reasonable functions $g$. In particular, we generalize the polynomial mean ergodic theorem for power bounded operators due to ter Elst and the second author \cite{tEM} to real polynomials and polynomial weights.
