积分方程之巴拿赫空间理论的形成

发布时间：2018-04-18 19:54

本文选题：积分方程 + 特征值　；参考：《西北大学》2015年博士论文

【摘要】：积分方程之巴拿赫空间理论是研究巴拿赫空间结构及定义在该空间中积分方程性质的理论,它不仅与许多数学分支有着密切的关系,而且在多方面都有非常重要的应用,因此,对积分方程之巴拿赫空间理论形成的历史进行研究,具有十分重要的理论意义和应用价值。本文在原始文献及相关研究文献的基础上,以“为什么数学”为研究依据,系统研究了积分方程理论对巴拿赫空间理论的形成的影响。所得结果如下：1.通过系统地分析积分方程特征值理论的形成与发展过程,可以发现积分方程特征值问题对巴拿赫空间理论的形成具有重要影响,是巴拿赫空间理论形成的一个重要因素。2.由巴拿赫空间理论应用的多样性,不难想到,导致巴拿赫空间理论形成的原因可能是多方面的,通过对与求解积分方程有关的“矩量问题”进行系统的研究,指出“矩量问题”也是导致巴拿赫空间理论形成的一个重要原因。3.深入细致地研究了各个数学家在赋范线性空间方面的工作,对巴拿赫空间理论的历史进行了较为详细地考察。确定了巴拿赫空间理论的优先权问题的重要性,并给出巴拿赫空间理论形成的判定条件为：导致巴拿赫空间理论产生的一个具体的数学问题、完备赋范空间概念的确定、在积分方程方面的应用。指出里斯的工作满足巴拿赫空间理论形成的所有判定条件,他对巴拿赫空间理论的形成具有重要影响。此外这里还从政治、民族和师承关系等角度,分析了社会因素对巴拿赫空间理论形成的影响,表明了巴拿赫空间理论是数学思想和现实世界的必然结果。4.提炼出了巴拿赫空间理论在数学各个领域中的影响。通过探讨该理论与一些基本理论之间的关系,清晰地罗列出该理论在各个数学理论中的作用,表明了巴拿赫空间理论在众多数学理论中的重要的地位,进而突出对该理论的形成过程进行研究的必要性。
[Abstract]:The Barnabian space theory of integral equations is a theory that studies the structure of Barnabian space and defines the properties of integral equations in this space. It not only has a close relationship with many branches of mathematics, but also has very important applications in many aspects.It is of great theoretical significance and application value to study the history of the formation of Barnabian space theory of integral equations.In this paper, based on the original literature and related research papers, the influence of integral equation theory on the formation of Barnabas space theory is systematically studied based on "why mathematics".The result is as follows: 1.By systematically analyzing the formation and development of the eigenvalue theory of integral equation, it is found that the eigenvalue problem of integral equation has an important influence on the formation of Barnabian space theory and is an important factor in the formation of Barnabian space theory.From the diversity of applications of Barnabas space theory, it is not difficult to imagine that the reasons leading to the formation of Barnabian space theory may be from many aspects. Through the systematic study of the "moment problem" related to the solution of integral equations,It is pointed out that "moment problem" is also an important reason for the formation of Barnabian space theory.The work of various mathematicians in normed linear space is studied in detail, and the history of Barnabas space theory is investigated in detail.The importance of the priority problem of Barnabas space theory is determined, and the conditions for the formation of the Panama space theory are as follows: a specific mathematical problem leading to the formation of the Panama space theory and the determination of the concept of complete normed space.Application in integral equation.It is pointed out that Reese's work satisfies all the criteria for the formation of Barnabas space theory, and he has an important influence on the formation of Barnabas space theory.In addition, this paper analyzes the influence of social factors on the formation of Panama's space theory from the angle of politics, nationality and the relationship between teachers and students, and shows that the theory of Panama's space is the inevitable result of mathematical thought and the real world.The influence of Barnabas space theory in various fields of mathematics is abstracted.By discussing the relationship between the theory and some basic theories, the role of the theory in various mathematical theories is clearly listed, which shows the important position of Barnabian space theory in many mathematical theories.Then the necessity of studying the formation process of the theory is highlighted.
【学位授予单位】：西北大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O177.2

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