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

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).

Anahtar Kelimeler:

Bases of cosines and sines, Sturm--Liouville equation

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

Keywords:

Bases of cosines and sines, Sturm--Liouville equation,

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Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, F.Agayev str., AZ1141, Baku-AZERBAIJAN e-mail: aahuseynli@gmail.com