Advanced Functional Analysis
Functional analysis is a fundamental course in mathematics. In this course, we will study basic contents on normed spaces and inner product spaces, as well as the theory of linear functionals and linear operators on these spaces, including Hahn Banach theorem, open mapping theory, closed image theorem, and the uniform boundedness principle. Furthermore, we will study the spectral theory of compact linear operators and self-adjoint operators.
Lecturer
Date
17th September ~ 31st December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 09:50 - 12:15 | Qiuzhen | - | - | - |
Reference
1. Erwin Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons,
1989.
2. Peter Lax, Functional Analysis, John Wiley & Sons, 2002.
3. 张恭庆，林源渠，泛函分析讲义（上册），北京大学出版社, 1987.
4. Walter Rudin，泛函分析，第二版，机械工业出版社, 2004.
5. Masamichi Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.
1989.
2. Peter Lax, Functional Analysis, John Wiley & Sons, 2002.
3. 张恭庆，林源渠，泛函分析讲义（上册），北京大学出版社, 1987.
4. Walter Rudin，泛函分析，第二版，机械工业出版社, 2004.
5. Masamichi Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Dr. Ngai received his B.Sc. from University of Hong Kong, and his M.A. and Ph.D. from University of Pittsburgh. After receiving his Ph.D., he has held research and teaching positions at The Chinese University of Hong Kong, Cornell University, Georgia Institute of Technology, and Georgia Southern University. He joined Beijing Institute of Mathematical Sciences and Applications as a professor in 2024. His main research areas are fractal geometry and the theory of fractal measures. He is also interested in the theories of wavelets, self-affine tiles, fractal differential equations, and spectral graph theory.