Department:
MATH
Course Number:
7337
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every odd fall semester
Fourier analysis in Euclidean space. Basic topics including L^1 and L^2 theory; advanced topics such as distribution theory, uncertainty, Littlewood-Paley theory
Prerequisites:
Course Text:
No text
Topic Outline:
- 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.
