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.


  • 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% developedEdit

Locally Compact Groups 0% developedEdit

Banach Spaces of a Locally Compact Group 0% developedEdit

Haar Measure and spaces 0% developedEdit

The Group algebra and the Regular Representation 0% developedEdit

Square Integrable Representations 0% developedEdit

Representations of Compact Groups 0% developedEdit

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

Direct Integral of Representations 0% developedEdit

Characters of Locally Compact Groups 0% developedEdit

The Dual of a Locally Compact Group 0% developedEdit

Plancherel Theorem 0% developedEdit

Plancherel Measure 0% developedEdit

Topic 1: Fell Bundles 0% developedEdit

Part 2 Reductive Groups:

Semi-simple Lie Groups 0% developedEdit

Reductive Groups 0% developedEdit

Appendices 0% developedEdit

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.