This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
Author(s): Jan van Neerven
Series: Cambridge Studies in Advanced Mathematics 201
Edition: 1
Publisher: Cambridge University Press
Year: 2022
Language: English
Pages: 712
Tags: Banach Spaces, Hilbert Spaces, Operator, Spectral Theory, Semigroups, Quantum Mechanics
1. Banach Spaces
2. The Classical Banach Spaces
3. Hilbert Spaces
4. Duality
5. Bounded Operators
6. Spectral Theory
7. Compact Operators
8. Bounded Operators on Hilbert Spaces
9. The Spectral Theorem for Bounded Normal Operators
10. The Spectral Theorem for Unbounded Normal Operators
11. Boundary Value Problems
12. Forms
13. Semigroups of Linear Operators
14. Trace Class Operators
15. States and Observables
