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Journal of Function Spaces and Applications
Volume 2012, Article ID 736437, 17 pages
http://dx.doi.org/10.1155/2012/736437
Research Article

Spectral Analysis of -Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition

Department of Mathematics, Nevsehir University, Nevsehir 50300, Turkey

Received 20 April 2012; Accepted 2 August 2012

Academic Editor: Feliz Minhós

Copyright © 2012 Aytekin Eryılmaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with -Sturm-Liouville boundary value problem in the Hilbert space with a spectral parameter in the boundary condition. We construct a self-adjoint dilation of the maximal dissipative -difference operator and its incoming and outcoming spectral representations, which make it possible to determine the scattering matrix of the dilation. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of operator generated by boundary value problem.