论文标题
关于。布鲁克（Bruck），证明采矿和渐近规律性的偏僻的平均值
R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces
论文作者
论文摘要
我们分析了布鲁克的证明，以获得均匀凸出的banach空间中cesàro的明显渐近规则性率。我们的费率仅取决于统一凸的标准和模量$η$。 Bruck证明的一种成分是Pisier的结果，Pisier的结果表明，每个均匀的凸（实际上每个均匀的非Quare）Banach Space都有一定的Rademacher型$ Q> 1 $，带有合适的常数$ C_Q $。我们明确确定$ q $和$ c_q $，这仅取决于我们模量的单个值$η（1）$。除了这些具体结果之外，我们总结了布鲁克的工作如何激发了证明挖掘计划中的发展，该计划应用了逻辑中的工具以在数学的各个领域中获得结果。
We analyze a proof of Bruck to obtain an explicit rate of asymptotic regularity for Cesàro means in uniformly convex Banach spaces. Our rate will only depend on a norm bound and a modulus $η$ of uniform convexity. One ingredient for the proof by Bruck is a result of Pisier, which shows that every uniformly convex (in fact every uniformly nonsquare) Banach space has some Rademacher type $q>1$ with a suitable constant $C_q$. We explicitly determine $q$ and $C_q$, which only depend on the single value $η(1)$ of our modulus. Beyond these specific results, we summarize how work of Bruck has inspired developments in the proof mining program, which applies tools from logic to obtain results in various areas of mathematics.
