Discrete Harmonic Analysis

Department: 
MATH
Course Number: 
8803-LAC
Hours - Lecture: 
3
Hours - Total Credit: 
3
Typical Scheduling: 
Not Regularly Scheduled
Prerequisites: 

Real Analysis

Course Text: 

TBA

Topic Outline: 

Discrete Harmonic Analysis studies averaging type operators, formulated over the integers. Their study in the integer setting becomes much more involved. One sees a hierarchical structure, exhibiting characteristics of the continuous and periodic versions of the questions, in the form of Gauss sums. This course will serve as an introduction to this topic. It engages harmonic analysis, analytic number theory, and arithmetic combinatorics.