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).
Bases of cosines and sines, Sturm--Liouville equation
"On the stability of basisness in L_p(1 < p < +\infty) of cosines and sines,"
Turkish Journal of Mathematics: Vol. 35:
1, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss1/5