Mathematical Sciences: Degree of Convergence of Eigenfunction Expansions

数学科学：本征函数展开式的收敛度

• 批准号: 9109444
• 金额: $ 1.8万
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9109444&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Degree; Convergence; Eigenfunction

In this project the principal investigator will initiate preliminary work to determine the feasibility of extending one- dimensional techniques to investigate the rates of convergence of two-dimensional Fourier series and more general eigenfunction expansions of Sturm-Liouville type. In particular, she will consider rates of convergence and the asymptotic behavior of partial sums of functions of bounded variation and functions whose derivatives have bounded variation. Problems involving eigenfunction expansions arise in a host of areas of applied mathematics and engineering. There are two basic questions that need to be answered. The first involves the rate of convergence of the expansion and the second involves the asymptotic behavior of the partial sums as the number of terms increases to infinity. The principal investigator plans on answering these questions for series expansions in two dimensions by extending techniques that have worked for series in one dimension.

在本项目中，主要研究者将启动 初步工作以确定延长一个的可行性- 三维技术，以调查收敛速度， 二维傅里叶级数和更一般的本征函数 Sturm-Liouville型展开式 特别是，她将 考虑收敛速度和渐近行为， 有界变差函数和 导数有界变差。 涉及本征函数展开的问题出现在一个主机的 应用数学和工程领域。 有两种基本 需要回答的问题 第一个涉及到 收敛的扩展和第二涉及渐近 部分和的行为随着项的数量增加到 无穷大. 首席研究员计划回答这些问题 二维级数展开式的问题 在一维序列中有效的技术。