弗雷德霍姆的首篇论文及其影响  

Research on Ivar Fredholm's First Paper and Its Influence

作　　者：王全来[1] WANG Quanlai(The College of Computer and Information Engineering, Tianjin Normal University, Tianjin 300387, Chin)

机构地区：[1]天津师范大学计算机与信息工程学院,天津300387

出　　处：《咸阳师范学院学报》2017年第2期1-5,共5页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(11571276)

摘　　要：运用历史分析和比较的方法,详细研究了弗雷德霍姆关于缺项级数方面的论文。该论文是其在学生时代完成的,深受当时学术环境的影响。论文中构造了缺项级数的例子,并用偏微分方程法证明了相应定理,其证明过程存在错误,直到1994年才被Khavinson D和Shapiro H S指出。在他的工作影响下,后续数学家做了大量工作,不仅构造了更大类的缺项级数,给出了具有普适性的缺项级数定理,而且继承和发展了他的证明方法。This paper first discusses Ivar Fredholm＇ s paper about gap series through historical analysis and comparative method. This paper was finished during his school days, and deeply affected by the academic environment at that time. Examples of gap series were constructed in this paper. It proved the corresponding gap theorem by the method of partial differential equation. There was an error in the proof, and was pointed by D. Khavinson and H. S. Shapiro until 1994. Under his influence, the later mathematicians have done a lot of work. They construct lager class of gap series and give better gap theorem, but also inherit and develop his proof＇s method.

关 键 词：弗雷德霍姆 缺项级数 解析开拓 热方程 

分 类 号：N09[自然科学总论—科学技术哲学]