Math 627, Introduction to Fourier Analysis

 

Syllabus:[pdf]

Schedule of material covered

1st week, Sept. 8-10   Origin of Fourier series: wave equation

2nd week, Sept. 13-18  Orthogonal sequences, trig. Fourier series and its properties

3rd week, Sept. 20-25 Fourier series, convolutions, Wiener's algebra

4th week, Sept. 27- Oct. 1 Convergence of Fourier series

5th week, Oct. 4-8             Convergence of Fourier series

6th week, Oct. 11-15         Convergence of Fourier series, Poisson kernel, Abel's summation

7th week, Oct. 18-22         Polynomial inequalities (Bernstein, Nikolskii) and applications

8th week, Oct. 25-29         Random and lacunary polynomials, Rudin-Shapiro polynomials

9th week, Nov. 1-5            Lacunary polynomials, Finite Fourier Analysis and FFT

10th week, Nov. 8-12         Fourier integrals

11th week, Nov. 15-19       Fourier integral and applications

12th week, Nov. 22-24       Fourier integral and applications, heat equation

13th week, Nov. 29- Dec. 3   Fourier integrals in higher dimension

14th week, Dec. 6- Dec. 10      Some applications

15th week, Dec. 13- Dec. 15    Some applications

 

Announcements:

 

For the HW, check the Canvas page