斯蒂尔杰斯矩量问题产生探源  

The Origin of Stieljes’ Moment Problem

作　　者：李威[1,2] 曲安京 LI Wei;QU Anjing(Institute for Advanced Study in the History of Science,Northwest University,Xi'an 70127,China;School of Statistics,Xi’an University of Finance of Economic,Xi'an 710100,China)

机构地区：[1]西北大学科学史高等研究院,西安710127 [2]西安财经大学统计学院,西安710100

出　　处：《中国科技史杂志》2022年第2期246-253,共8页The Chinese Journal for the History of Science and Technology

基　　金：国家自然科学基金资助项目“巴拿赫空间理论形成的历史研究”(项目编号:11901444);陕西省自然科学基础研究计划项目“线性积分方程理论历史研究”(项目编号:2019JQ-870);陕西省教育厅科研计划项目“大数据背景下巴拿赫空间理论在中国传播的可视化研究”(项目编号:19JK0326)。

摘　　要：矩量问题是概率论与数理统计的重要内容,也是寻求矩阵论和算子理论起源的线索之一。斯蒂尔杰斯矩量问题是矩量问题的开端,其思想可以追溯到连分数敛散性问题。文章深入分析连分数理论与发散级数之间的关系,探寻斯蒂尔杰斯积分的思想起源和创立过程;通过深入剖析矩量问题的确定性与其对应的连分数收敛性之间内在的思想关联,找出斯蒂尔杰斯研究矩量问题的产生动因。通过对斯蒂尔杰斯积分和斯蒂尔杰斯矩量问题历史发展过程的研究,可以寻求矩量问题理论发展的起源,同时为研究线性积分方程理论形成提供一个窗口。The moment problem is an important part of probability theory and mathematical statistics, and also one of the ways to explore the origin of matrix theory and operator theory.As the beginning of the problem of moments, the idea of Stieljes’ moment problem can be traced back to the problem of convergence and divergence of continued fractions.This paper analyzes the relationship between continued fraction theory and divergent series, explores the ideological origin and the founding process of Stieljes’ integral, and finds out the reason why Stieljes explores the moment problem by analyzing the internal ideological relationship between the moment problem determinacy and its corresponding convergence of continued fraction. Through the study of the historical development process of Stieljes’ integral and moment problem, we can find the origin of the development of moment problem theory, and provide a window for the study of the formation of linear integral equation theory.

关 键 词：矩量问题 连分数 斯蒂尔杰斯积分 黎曼积分 

分 类 号：N092[自然科学总论—科学技术哲学] O174.43[理学—数学]