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
- Hints
- Answers
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 $L^{p}$ spaces edit

The Group algebra and the Regular Representation edit

Square Integrable Representations edit

Representations of Compact Groups edit

The Group $C^{*}$ -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.