Fourier analysis in Euclidean space. Basic topics including L^1 and L^2 theory; advanced topics such as distribution theory, uncertainty, Littlewood-Paley theory
- L^1 theory: definition of the Fourier transform, dualities between decay and smoothness, approximate identities, inversion formulas
- L^2 theory: Schwartz space, Plancherel and Parseval's theorems, Paley-Wiener theorem, Hausdorff-Young
- Fourier transforms of distributions and measures
- Advanced topics, according to instructor's interest: for example, uncertainty principles, Littlewood-Paley theory, ideal theory, phase-space or local Fourier analysis, frames, pseudodifferential operator theory, sampling theory wavelets, Fourier series, etc.