On basicity of the system of eigenfunctions of one discontinuous spectral problem for second order differential equation for grand-Lebesgue space

Authors

YUSUF ZEREN
MIQDAD ISMAILOV
FATİH ŞİRİN

DOI

10.3906/mat-2003-20

Abstract

Basicity of the system of eigenfunctions of some\textbf{ }discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space $L_{p)} (-1;1)$ is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace $G_{p)} (-1;1)$ of $L_{p)} (-1;1)$ generated by shift operator is considered. Basicity of the system of eigenfunctions for the space $G_{p)} (-1;1)\oplus C$, $1

Keywords

Grand Lebesgue space, eigenfunctions, basicity, completeness, minimality, discontinuous spectral problem

First Page

1595

Last Page

1611

Recommended Citation

ZEREN, YUSUF; ISMAILOV, MIQDAD; and ŞİRİN, FATİH (2020) "On basicity of the system of eigenfunctions of one discontinuous spectral problem for second order differential equation for grand-Lebesgue space," Turkish Journal of Mathematics: Vol. 44: No. 5, Article 6. https://doi.org/10.3906/mat-2003-20
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/6