TY  - JOUR
TI  - On basicity of the system of eigenfunctions of one discontinuous spectral problem
for second order differential equation for grand-Lebesgue space
AB  - Basicity of the system of eigenfunctions of some discontinuous spectral problem for a second order differential
equation with spectral parameter in boundary condition for grand-Lebesgue space Lp)(−1; 1) is studied in this work.
Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace Gp)(−1; 1) of
Lp)(−1; 1) generated by shift operator is considered. Basicity of the system of eigenfunctions for the space Gp)(−1; 1)⊕C ,
1 < p < +∞, is proved. It is shown that the system of eigenfunctions of considered problem forms a basis for Gp)(−1; 1),
1 < p < +∞, after removal of any of its even-numbered functions.
AU  - ISMAILOV, Migdad
AU  - Zeren, Yusuf
AU  - SIRIN, FATIH
DO  - 10.3906/mat-2003-20
PY  - 2020
JO  - Turkish Journal of Mathematics
VL  - 44
IS  - 5
SN  - 1300-0098
SP  - 1595
EP  - 1611
DB  - TRDizin
UR  - http://search/yayin/detay/527754
ER  -