Spectral analysis of q-fractional Sturm-Liouville operators

Abstract

In this article, we study q-fractional Sturm-Liouville operators. Using by the functional method, we pass to a new operator. Then, showing that this operator is a maximal operator and constructing a self-adjoint dilation of the maximal dissipative operator. We prove a theorem on the completeness of the system of eigenvectors and associated vectors of the dissipative q-fractional Sturm-Liouville operators.

Keywords

• Dissipative q-fractional Sturm-Liouville operator
• dilation
• eigenvector
• scattering matrix
• functional model
• characteristic function