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Mathematical Communications, Vol. 19 No. 1, 2014.

Original scientific paper

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

Hüseyin Tuna orcid id orcid.org/0000-0001-7240-8687 ; Department of Mathematics, Mehmet Akif Ersoy University, Burdur, Turkey
Aytekin Eryılmaz ; Department of Mathematics, Nevşehir University, Neveşhir, Turkey

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Abstract

In this paper, we study $q$-Sturm-Liouville operators. We construct
a space of boundary values of the minimal operator and describe all
maximal dissipative, maximal accretive, self-adjoint and other
extensions of $q$-Sturm-Liouville operators in terms of boundary
conditions. Then we prove a theorem on completeness of the system
of eigenfunctions and associated functions of dissipative operators
by using the Lidskii's theorem.

Keywords

$q$-Sturm-Liouville operator; dissipative operator; completeness of the system of eigenvectors and associated vectors; Lidskii's theorem

Hrčak ID:

121826

URI

https://hrcak.srce.hr/121826

Publication date:

26.5.2014.

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