Functional Analysis/Harmonic Analysis
Introduction edit
Harmonic Analysis is the study of the decomposition of representations of abstract algebraic structures acting on topological vector spaces.
Note: A table of the math symbols used below and their definitions is available in the Appendix.
- Foreword
- Old Introduction
- Manual of Style – How to read this wikibook
- The set theory notation and mathematical proofs, from the book Mathematical Proof
- The experience of working with calculus concepts, from the book Calculus
Part 1: General theory of Locally Compact Groups.
Topological Groups edit
- Exercises
- Topological Group - Definition and elementary properties.
Locally Compact Groups edit
- Locally Compact Groups - Definition and Elementary Properties
Banach Spaces of a Locally Compact Group edit
Haar Measure and spaces edit
The Group algebra and the Regular Representation edit
Square Integrable Representations edit
Representations of Compact Groups edit
The Group -algebra and the Group Von Neumann algebra edit
Direct Integral of Representations edit
Characters of Locally Compact Groups edit
The Dual of a Locally Compact Group edit
Plancherel Theorem edit
Plancherel Measure edit
Topic 1: Fell Bundles edit
Part 2 Reductive Groups:
Semi-simple Lie Groups edit
Reductive Groups edit
Appendices edit
Here, you will find a list of unsorted chapters. Some of them listed here are highly advanced topics, while others are tools to aid you on your mathematical journey. Since this is the last heading for the wikibook, the necessary book endings are also located here.