Journals / Turkish Journal of Mathematics / 2011 / Cilt: 35 - Sayı: 1
On the stability of basisness in Lp(1 < p < +\infty) of cosines and sines
- Pages
- 47–54
- DOI
- —
Abstract
We study the basis properties in Lp(0, p) (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 Lp(0, p) (1 < p < \infty) and then show that the solution system above forms a basis in Lp(0, p) if and only if certain cosine system (or sine system, depending on type of initial conditions) forms a basis in Lp(0, p).
Özet
We study the basis properties in Lp(0, p) (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 Lp(0, p) (1 < p < \infty) and then show that the solution system above forms a basis in Lp(0, p) if and only if certain cosine system (or sine system, depending on type of initial conditions) forms a basis in Lp(0, p).