Analysis 3, Functional analysis.

Orthogonal series, convergence in L² norm and pointwise, Rademacher-Menshov theorem, Weyl sequence, trigonometric Fourier series, pointwise convergence, Dirichlet kernel, Riemann-Lebesgue lemma, Riemann's localization theorem, Kolmogorov's counterexample, Fejér kernel, Fejér's theorem, Carleson's theorem, Stone's theorem, Stone-Weierstrass theorem, abstract Fourier series, convergence of Fourier series.