The basis property in $L_p$ of the boundary value problem rationally dependent on the eigenparameter

@article{N2006,
abstract = {We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in $L_\{p\}$ of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in $L_\{p\}$ we use F. Riesz’s theorem.},
author = {N. B. Kerimov, Y. N. Aliyev},
journal = {Studia Mathematica},
keywords = {Sturm-Liouville; eigenparameter-dependent boundary conditions; basis; minimal system; quadratically close systems},
language = {eng},
number = {2},
pages = {201-212},
title = {The basis property in $L_\{p\}$ of the boundary value problem rationally dependent on the eigenparameter},
url = {http://eudml.org/doc/284470},
volume = {174},
year = {2006},
}

TY - JOUR
AU - N. B. Kerimov
AU - Y. N. Aliyev
TI - The basis property in $L_{p}$ of the boundary value problem rationally dependent on the eigenparameter
JO - Studia Mathematica
PY - 2006
VL - 174
IS - 2
SP - 201
EP - 212
AB - We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in $L_{p}$ of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in $L_{p}$ we use F. Riesz’s theorem.
LA - eng
KW - Sturm-Liouville; eigenparameter-dependent boundary conditions; basis; minimal system; quadratically close systems
UR - http://eudml.org/doc/284470
ER -