Introduction to Functional Analysis

Author: Zhao Huanguang
Publisher:
Publish Date: 2005-06-01
Features: "Functional" is a term introduced by the French mathematician Hadamard (1865-1963) in 1897 while studying variational problems. "Functional" is also known as "functional function," which is an extension or development of the concept of real (complex) valued functions. In terms, a functional is a function whose variable is a function. Its basic idea is to regard functions (or curves, etc.) as elements or points in a space, while the set of functions constitutes the space. "Functional analysis" is a modern branch of mathematics that studies the topological properties of infinite-dimensional linear spaces and the general properties of "functionals" and "operators." It is an important part of infinite-dimensional analysis. This book introduces the introductory knowledge of linear functional analysis, divided into six chapters, including: metric spaces, normed linear spaces, inner product spaces, bounded linear operators and bounded linear functionals, spectral analysis of bounded linear operators, and generalized functions and Sobolev spaces. This book can be used as a textbook or reference book for master's students who have not yet learned the basic functional analysis, or as a textbook or reference book for senior undergraduate students in mathematics departments.