泛函分析简介。英语泛函分析简。英语.docVIP

Functional Analysis Department of Mathematics, School of science, Xian University of Architecture and Technology, P.R.China, 710055 Abstract: Functional analysis is an emerging discipline，has a long history, as well as an important subject of analysis. The development of the functional analysis could divided into three stages.This paper introduce its origin, history of development and application.And introduces some domestic functional analysis of the main characters. Keywords: Functional analysis；Origin；History of development; Application. AMS:O47LXX 1.The origin of functional analysis Functional analysis is a new discipline, was officially listed in Germany abstract mathematics in 1932. The word functional analysis first appeared in the book a course of functional analysis which was published by levy (P. Levy, 1886-1971) in1922. It is a subject of analysis, but is different with the traditional discipline of analysis, the latter emphasizes the calculus, but the former emphasizes the concept. Also they have different objects, the latter focuses on the nature of the individual function (class), while the former focuses on the function space and its collection of operators, especially, its structure of topology, algebraic and sequence. But its hard to say that it has a unified object and goal. Functional analysis can be roughly divided into four areas: the first is the theory of function space, which from Hilbert spaces and Banach spaces to the theory of general linear topological spaces. The second is the analysis of the function spaces, this is the first part of the development, namely so-called functional calculus. The third is a mapping between function spaces and the theory of operator, it is the most mature of development that the theory of linear operators in a Hilbert space. The fourth is the algebraic structures of operators (or function) set, such as Banach algebras, Von Neumann algebras, algebras and the theory of operator semi-group. The origin of F