1. A survey of the approximation approaches to the Riemann Hypothesis (RH) - N.Wiener, R.Salem, N.Levinson, B.Nyman, A.Beurling, L.Baez-Duarte, M.Balazard, and others.

2. B.Nyman's equivalent form of the RH.

3. The periodic dilations problem and the Bohr transform.

4. Geometry of the dilated systems through examples (binomials, Kozlov's indicator functions, etc.).