# Functional Analysis/Harmonic Analysis

## IntroductionEdit

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.