SUBJECT
Title
Function series
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Pointwise and L^2 norm convergence of orthogonal series. Rademacher-Menshoff theorem. Weyl-sequence. Pointwise convergence of trigonometric Fourier-series. Dirichlet integral. Riemann-Lebesgue lemma. Riemann’s localization theorem for Fourier-series. Local convergence theorems. Kolmogorov’s counterexample. Fejér’s integral. Fejér’s theorem. Carleson’s theorem.
Readings
- Bela Szokefalvi-Nagy: Introduction to real functions and orthogonal expansions,
- Natanszon: Constructive function theory