Functional Analysis/Harmonic Analysis

Introduction[edit | edit source]

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 | edit source]

Exercises
- Hints
- Answers
Topological Group - Definition and elementary properties.

Locally Compact Groups [edit | edit source]

Locally Compact Groups - Definition and Elementary Properties

Banach Spaces of a Locally Compact Group [edit | edit source]

Haar Measure and $L^{p}$ spaces [edit | edit source]

The Group algebra and the Regular Representation [edit | edit source]

Square Integrable Representations [edit | edit source]

Representations of Compact Groups [edit | edit source]

The Group $C^{*}$ -algebra and the Group Von Neumann algebra [edit | edit source]

Direct Integral of Representations [edit | edit source]

Characters of Locally Compact Groups [edit | edit source]

The Dual of a Locally Compact Group [edit | edit source]

Plancherel Theorem [edit | edit source]

Plancherel Measure [edit | edit source]

Topic 1: Fell Bundles [edit | edit source]

Part 2 Reductive Groups:

Semi-simple Lie Groups [edit | edit source]

Reductive Groups [edit | edit source]

Appendices [edit | edit source]

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.