Mathematics MA342A, Harmonic Analysis I
Notes
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.)