Search Results
You are looking at 1 - 2 of 2 items for
- Author or Editor: Aytekin Eryilmaz x
- Refine by Access: All Content x
This paper is devoted to studying a q-analogue of Sturm-Liouville operators. We formulate a dissipative q-difference operator in a Hilbert space. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which is based on the method of Pavlov and define its characteristic function. Finally, we prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative q-Sturm-Liouville difference operator.
In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livšic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.
