关于解剖算子的基本定理基础数学专业论文.docxVIP

哈尔滨 哈尔滨工业大学理学硕士学位论文 - - II - Abstract In twenty century, functional analysis was mostly influenced by quantum mechanics related mathematical problem’s research, and developed continuously which has formed classical functional analysis theory. Thereinto, the “Uniform Boundedness Principle ”、 the “ Open Mapping Theorem ” and the “ Hahn- Banach theorem”are praised as the “three basic theorem”. It is went without saying that the effect they produced in theory and in application is very large. At the same time, along with the development of science, the classical theory exposes many localization gradually. Because the three theorems aim at the linear operators, they can not be applied directly in many cases. Therefore they can only be applied in those excessively ideal cases. It leads that the development of many related theory ,such as differential equation 、 congruity analysis, is restricted. And it blocks the more development of quantum mechanics, too. The nonlinear problem has become the mainstream of all subjects in the contemporary era. Because the nonlinear problem may be come down to the operator equations leaded by nonlinear operators, the research about the operator theory attracted many attentions the near twenty years. However the research about the basic functional analysis theorems aiming to the nonlinear operators is very few. Considering such instance, for the dissecting mappings which include all linear operators and some nonlinear operators, the article establishes the “ Equicontinuity Principle ” , and improves the “ Uniform Boundedness Principle ” with some related basic theorems at the same time, and gives another proof for the Uniform Boundedness Principle of the set of continuous nonlinear mapping ????F1, X ?X ,Y ???A1 ?X ,Y ?. Keywords Topological vector Space ； Seminormed space; Dissecting mapping；Equicontinuity principle - - PAGE IV- 目 录 摘 要 I Abstract II 第 1 章 绪论 1 1.1 引言 1 1.2 课题