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Trinity College Dublin

TCD Mathematics

School of Mathematics

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.)