We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in 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 we use F. Riesz’s theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-2-6,
author = {N. B. Kerimov and Y. N. Aliyev},
title = {The basis property in $L\_{p}$ of the boundary value problem rationally dependent on the eigenparameter},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {201-212},
zbl = {1106.34056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-2-6}
}
N. B. Kerimov; Y. N. Aliyev. The basis property in $L_{p}$ of the boundary value problem rationally dependent on the eigenparameter. Studia Mathematica, Tome 173 (2006) pp. 201-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-2-6/