Lectures: 9.30am-10:45am on Tuesdays, Thursdays, in CSI 4122

Office Hour: Monday, 5:00pm-6:00pm on Zoom (or by appointment otherwise).

Assignments: Homework must be submitted on the date assigned. Homework must be prepared without consulting any other person. You may however consult any written reference. In this case you should cite the reference. Results taken from the reference should be (re)stated to the notation used in the course. Explanation should be given in complete English sentences. Written work must be legible and clear.

Description: MATH 634 Harmonic Analysis is the graduate level course in mathematics that continuous MATH 630 Real Analysis I, MATH 631 Real Analysis II and MATH 632 Functional Analysis. Topics include: Fourier series and Fourier transform: L1 theory: Dirichlet and Fejer theorems, inversion theorem L2 theory: Plancherel-Parseval theorems, Paley-Wiener theorem. Lp theory: Hausdorff-Young theorem. Distribution theory - Schwartz theory, almost periodic functions. Square integrable group representations: Windowed Fourier tranforms and Wavelets; Gabor frames; Wavelet frames/ONB; additional topics as time permits.

Grading: 25% Homeworks ; 25% Mid-Term Exam ; 50% Final Exam

References: Recommended textbooks:
1. Harmonic Analysis, B. Simon (vol. 3 of the 5-volume set)
2. Harmonic Analysis and Applications, J.Benedetto
3. Fourier Analysis, Stein and Shakarchi (one volume from the set of 4 books)
4. A First Course in Fourier Analysis, Kammler