Abstract: | The completeness, minimality, and basis property in L 20, π] and L p0, π], p ≠ 2, are considered for systems of dilated functions u n (x) = S(nx), n ∈ N, where S is the trigonometric polynomial S(x) = Σ k=0 m a k sin(kx), a 0 a m ≠ 0. A series of results are presented and several unanswered questions are mentioned. |