Systems of dilated functions: Completeness, minimality, basisness

Аннотация

The completeness, minimality, and basis property in L²[0, π] and L^p[0, 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^ma_ksin(kx), a₀a_m ≠ 0. A series of results are presented and several unanswered questions are mentioned.