Ali A. HUSEYNLI

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,

PDF

___

He, X., Volkmer, H.: Riesz bases of solutions of Sturm–Lioville equations. The Journal of Fourier Analysis and Applications 7(3), 297-307 (2001).
Kadec, M.I.: The exact value of the Paley-Wiener constant. Dokl. Akad. Nauk SSSR 155, 1253-1254 (1964), English translation: Sov. Math. Dokl. 5, 559-561 (1964).
Levin, B.Ya.: Distribution of zeros of entire functions. Amer. Math. Soc. Translations of Mathemaical Monographs, Vol.5 (1980).
Levinson, N.: Gap and Density Theorems. AMS. Col. Public. 26 (1940).
Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, Vol. I. Springer 1977.
Marchenko, V.A.: Sturm–Liouville operators and their applications. Kiev. Naukova Dumka 1977.
Paley, R.E., Wiener, N.: Fourier transforms in the complex domain. AMS. Col. Public. Vol. 19. 1934.
Redheﬀer, R.M., Young, R.M.: Completeness and basis properties of complex exponentials. Trans. Amer. Math. Soc. 277, 93-111 (1983).
Sedletskii, A.M.: Fourier transforms and approximations. Amsterdam. Gordon and Breach Science Publ. 2000.
Sedletskii, A.M.: Classes of analytic Fourier transforms and exponential approximations. Moscow. Physmatlit 2005.
Young, R.M.: An Introduction to Nonharmonic Fourier Series. Academic Press 1980.
Zygmund, A.: Trigonometric series, Vol. II. Cambridge University Press 1959. Ali A. HUSEYNLI
Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, F.Agayev str., AZ1141, Baku-AZERBAIJAN e-mail: aahuseynli@gmail.com