Mathematics MA342A, Harmonic Analysis I
Some (not all) parts of the course notes will be in the form of a handout or will be available here. All will be in PDF format and require a programme such as Adobe Acrobat Reader to read them.
- Chapter 1: Examples for Fourier analysis
Review: Fourier series.
The unit circle.
Topologocal abelian groups.
Finite abelian groups.
Real line. Integers.
- Chapter 2: Convergence theorems
Convergence results for Fourier series on the circle.
- Chapter 3: LCA groups and their duals
- The abstract setting for Fourier analysis on groups: the class of LCA groups, the topology of the dual group, Pontryagin duality, Haar measure, Fourier transform in general, Plancherel theorem. (Most proof omitted.)