Functional Analysis

A comprehensive, graduate-level introduction to functional analysis covering both the theory and main applications, with over 300 exercises.

Jan van Neerven (Author)

9781009232470, Cambridge University Press

Hardback, published 7 July 2022

650 pages
23.5 x 15.7 x 4.9 cm, 1.23 kg

'One of its strengths is that it is a genuine textbook rather than a reference text. It is highly readable and pedagogical, giving a good level of detail in proofs, but staying concise and keeping its story clear rather than being encyclopedic. Another strength of the textbook is that it is well motivated by applications of functional analysis to other areas of mathematics, with a special emphasis on partial differential equations and quantum mechanics throughout the book.' Pierre Portal, zbMATH

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.

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
Appendix A. Zorn's lemma
Appendix B. Tensor products
Appendix C. Topological spaces
Appendix D. Metric spaces
Appendix E. Measure spaces
Appendix F. Integration
Appendix G. Notes
References
Index.

Subject Areas: Mathematical physics [PHU], Functional analysis & transforms [PBKF]