In this paper, we study $q$-Sturm-Liouville operators. We constructa space of boundary values of the minimal operator and describe allmaximal dissipative, maximal accretive, self-adjoint and otherextensions of $q$-Sturm-Liouville operators in terms of boundaryconditions. Then we proved a theorem on completeness of the systemof eigenfunctions and associated functions of dissipative operatorsby using the Lidskii's theorem.
Publié le : 2014-06-10
Classification:
$q$-Sturm-Liouville operator, Dissipative operator, Completeness of the system of eigenvectors and associated vectors, Lidskii's theorem.,
34L10, 39A13.
@article{mc316,
author = {Tuna, H\"useyin and Ery\i lmaz, Aytekin},
title = {Completeness of the system of root functions of $q$-Sturm-Liouville operators},
journal = {Mathematical Communications},
volume = {19},
number = {1},
year = {2014},
pages = { 65-73},
language = {eng},
url = {http://dml.mathdoc.fr/item/mc316}
}
Tuna, Hüseyin; Eryılmaz, Aytekin. Completeness of the system of root functions of $q$-Sturm-Liouville operators. Mathematical Communications, Tome 19 (2014) no. 1, pp. 65-73. http://gdmltest.u-ga.fr/item/mc316/