We consider Sturm-Liouville problems with a boundary condition linearly dependent on the eigenparameter. We study the case of decreasing dependence where non-real and multiple eigenvalues are possible. By determining the explicit form of a biorthogonal system, we prove that the system of root (i.e. eigen and associated) functions, with an arbitrary element removed, is a minimal system in L₂(0,1), except for some cases where this system is neither complete nor minimal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-12,
author = {Y. N. Aliyev},
title = {Minimality of the system of root functions of Sturm-Liouville problems with decreasing affine boundary conditions},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {147-162},
zbl = {1133.34371},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-12}
}
Y. N. Aliyev. Minimality of the system of root functions of Sturm-Liouville problems with decreasing affine boundary conditions. Colloquium Mathematicae, Tome 107 (2007) pp. 147-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-12/