Math 890 - Fourier Analysis

Math 890 - "Fourier Analysis" - 26476

TTh 7:35 - 8:50 a.m. -- 302 Snow

Instructor: Rodolfo H. Torres

Office: 546 Snow

tel: 864-7310

e-mail: torres "AT" math.ku.edu

Homepage: www.math.ku.edu/~torres

Course Description:

Fourier analysis is a tremendous tool to study many problems in both theoretical and applied mathematics. Its discrete and numerical version, the fast Fourier transform (FFT), is arguably one he most important contribution of mathematics to our every day life; specially nowadays with the use of computers and the fast exchange of information. Every time you download an image from the web some version of Fourier analysis is involved. The course will focus on theoretical topics about the characterization of function spaces (for example Sobolev and other "fractional derivative" spaces and spaces of distributions) and the study of operators (singular integrals, pseudo-differential operators, etc), but I will also try to present and idea of why some of these analytical tools turned out to be so useful in other areas. Depending on time, I will cover material about wavelets and other time-frequency techniques in Fourier analysis developed in the last two decades and which continued to be actively investigated today. These tools permit a more refined multiscale analysis of functions (or signals) and the transformations that act on them than "classical" Fourier analysis. This class will be most useful to students in analysis, differential equations, probability, numerical analysis and other branches of applied math, but it could be of interest too to students in other areas who want to learn more about some other mathematics outside their immediate field of research. The course will be tailored in part to the background of the students enrolled.

Prerequisites:

Math 810 or permission of the instructor.