Fourier Analysis

The course is intended to give the students a thorough introduction to Fourier analysis. Topics that are covered are: Fourier series and Fourier integrals; pointwise, uniform, and mean convergence of Fourier series; approximation kernels; Parseval's identity and Bessel's inequality; Plancherel's identity; the Schwartz space, convolutions, the Poisson summation formula, Heisenberg's uncertainty principle, selected applications in mathematics (for example partial differential equations and number theory) and in technology (for example signal processing). Topics that may be included in the course: Fourier transforms of distributions, discrete Fourier transforms, Fast Fourier Transform, filter theory, wavelets.

1. Knowledge: The student has a knowledge of concepts and methods from Fourier analysis, as specified under "academic content".

2. Skills: The student is able to apply his or her knowledge of Fourier analysis to solve mathematical and technological problems.

Lectures and exercises.