On the stability of basisness in L_p(1 p +\infty) of cosines and sines

Abstract

We study the basis properties in L_p(0, \pi) (1 < p < \infty) 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 L_p(0, \pi) (1 < p < \infty) and then show that the solution system above forms a basis in L_p(0, \pi) if and only if certain cosine system (or sine system, depending on type of initial conditions) forms a basis in L_p(0, \pi).