Completeness of the system of root functions of $q$-Sturm-Liouville operators

Hüseyin Tuna; Aytekin Eryılmaz

Vol. 19 No. 1 (2014)

Regular Articles

Completeness of the system of root functions of $q$-Sturm-Liouville operators

Published 2014-01-07

Hüseyin Tuna
Aytekin Eryılmaz

Hüseyin Tuna

Aytekin Eryılmaz
Nevşehir University, Nevşehir/TURKEY

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Abstract

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.

Keywords

$q$-Sturm-Liouville operator, Dissipative operator, Completeness of the system of eigenvectors and associated vectors, Lidskii's theorem.

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Author Biography

Aytekin Eryılmaz

Dept. Maths.