Mathematical Sciences: Problems in Almost Everywhere Convergence of Weighted Averages and in Spherical Type of Rank One Transformations

数学科学：加权平均几乎处处收敛的问题和一阶变换的球型问题

• 批准号: 9307945
• 负责人: Karin Reinhold-Larsson
• 金额: $ 2.87万
• 依托单位: SUNY at Albany
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307945&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Almost; Everywhere

This research will focus on two topics: (1) the almost everywhere convergence of weighted averages, and (2) spectral type of rank one transformations. The first problem operators on probability spaces and the study of sequences of measures for which the corresponding operators fail to converge. In the second study, rank one transformations has been a source of numerous and important examples in ergodic theory; however, their spectral type has not been studied in depth. This research is in the general area of modern analysis where researchers examine the theory of operators and transformations on various spaces of finite and infinite dimension.

本文主要研究两个问题：(1)加权平均的几乎处处收敛性；(2)一阶变换的谱型。概率空间上的第一类算子及其算子不收敛的测度序列的研究。在第二个研究中，一级变换已经成为遍历理论中许多重要例子的来源；然而，它们的光谱类型尚未被深入研究。这项研究是现代分析的一般领域，研究人员在有限和无限维的各种空间上研究算子和变换的理论。