Harmonic Analysis

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.