Applied Functional Analysis

Author: Xu Tianzhou
Publisher:
Publish Date: 2003-05-01
Features: This book is rich in content, easy to understand, practical, and beneficial for self-study. It can serve as a textbook or teaching reference for senior undergraduate and graduate students in science and engineering disciplines in higher education institutions. It can also be read by researchers and engineering technicians interested in functional analysis. This book is written as a textbook for engineering graduate students studying the course "Applied Functional Analysis." The book is divided into eight chapters, covering the following topics: Foundations of Real Analysis, Metric Spaces, Normed Linear Spaces and Banach Spaces, Inner Product Spaces and Hilbert Spaces, General Theory of Linear Operators, Spectral Theory, Calculus on Banach Spaces, and Linear Operator Semigroups. The book focuses on explaining the essential differences between finite-dimensional and infinite-dimensional analysis, using examples to illustrate various abstract concepts and theorems. This helps readers understand the basic ideas, theories, and methods for solving problems in infinite-dimensional spaces, especially the important roles of compactness, self-adjointness, and compressibility in infinite-dimensional analysis. The book is accompanied by a substantial number of exercises and hints to provide readers with the necessary training to master functional analysis methods.