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.


  • 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 0% developed

edit

Locally Compact Groups 0% developed

edit

Banach Spaces of a Locally Compact Group 0% developed

edit

Haar Measure and spaces 0% developed

edit

The Group algebra and the Regular Representation 0% developed

edit

Square Integrable Representations 0% developed

edit

Representations of Compact Groups 0% developed

edit

The Group -algebra and the Group Von Neumann algebra 0% developed

edit

Direct Integral of Representations 0% developed

edit

Characters of Locally Compact Groups 0% developed

edit

The Dual of a Locally Compact Group 0% developed

edit

Plancherel Theorem 0% developed

edit

Plancherel Measure 0% developed

edit

Topic 1: Fell Bundles 0% developed

edit

Part 2 Reductive Groups:

Semi-simple Lie Groups 0% developed

edit

Reductive Groups 0% developed

edit

Appendices 0% developed

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.