< Functional Analysis
Introduction
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
- Exercises
- Hints
- Answers
- Topological Group - Definition and elementary properties.
Locally Compact Groups
- Locally Compact Groups - Definition and Elementary Properties
Banach Spaces of a Locally Compact Group
Haar Measure and spaces
The Group algebra and the Regular Representation
Square Integrable Representations
Representations of Compact Groups
The Group -algebra and the Group Von Neumann algebra
Direct Integral of Representations
Characters of Locally Compact Groups
The Dual of a Locally Compact Group
Plancherel Theorem
Plancherel Measure
Topic 1: Fell Bundles
Part 2 Reductive Groups:
Semi-simple Lie Groups
Reductive Groups
Appendices
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.
- List of Mathematical Symbols
- List of Theorems
- References
- Index
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