Abstract Harmonic Analysis
Locally compact groups, Pontryagin duality, and representation-theoretic Fourier analysis.
Abstract Harmonic Analysis. Locally compact groups, Pontryagin duality, and representation-theoretic Fourier analysis.
Foundations and canonical references
The standard treatments of abstract harmonic analysis approach the subject from complementary angles. Folland, A Course in Abstract Harmonic Analysis (2016) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Hewitt, Abstract Harmonic Analysis I (1979) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for abstract harmonic analysis include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2016A Course in Abstract Harmonic Analysisfolland-2016
- textbook · primary · 1979Abstract Harmonic Analysis Ihewitt-1979, ross-1979
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