Functional Analysis/Harmonic Analysis
Introduction
editHarmonic 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
editHaar Measure and spaces
editThe Group algebra and the Regular Representation
editSquare Integrable Representations
editRepresentations of Compact Groups
editThe Group -algebra and the Group Von Neumann algebra
editDirect Integral of Representations
editCharacters of Locally Compact Groups
editThe Dual of a Locally Compact Group
editPlancherel Theorem
editPlancherel Measure
editTopic 1: Fell Bundles
editPart 2 Reductive Groups:
Semi-simple Lie Groups
editReductive Groups
editAppendices
editHere, 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.