Fourier Analysis
A.Y. 2018/2019
Learning objectives
The course gives the basis about the classical theory on the Fourier series and the Fourier transform both in the 1-dimensional case and in several dimensions.
Expected learning outcomes
Learning the basics facts about the convergence and the summability of Fourier series; properties of the Fourier transform when defined on principal function spaces and on distributions.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Fourier series in one dimension. Principal properties of Fourier coefficients. Fejer and Dirichlet kernels, summability in norm and pointwise summability. Fourier transform in R and in R^n. Theory L^1 and L^2. Spaces of Schwartz functions S and of tempered distributions S' and Fourier transforms in S and S'. L^p theory. Hilbert trasform and singular integrals. Fourier multipliers and boundedness in L^p. Fourier series in more dimensions and norm convergence in L^p. Introduction to wavelets: Haar and Shannon wavelets. Gabor transform.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Lessons: 42 hours
Professor:
Salvatori Maura Elisabetta
Professor(s)