  We discuss completeness, minimality, and basisness, in $L^2[0, \pi]$ and
$L^p[0, \pi]$, $p \neq 2$, of dilated systems $u_n(x) = S(nx)$, $n \in
\mathbb{N}$, where $S$ is a trigonometric polynomial
  $S(x) = \sum_{k = 0}^m a_k \sin(kx), \quad a_0 a_m \neq 0.$
  We will present some results and mention a few unsolved questions.
