On the stability of basisness in Lp (1 <p< +∞) of cosines and sines

Abstract

We study the basis properties in Lp(0, π) (1 <p< ∞) of the solution system of Sturm–Liouville equations with different types of initial conditions. We first establish some results on the stability of the basis property of cosines and sines in Lp(0, π) (1 <p< ∞) and then show that the solution system above forms a basis in Lp(0, π) if and only if certain cosine system (or sine system, depending on type of initial conditions) forms a basis in Lp(0, π).