Abstract and Applied Analysis
Volume 2011 (2011), Article ID 608329, 10 pages
http://dx.doi.org/10.1155/2011/608329
Research Article

Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions

Murat Olgun, Turhan Koprubasi, and Yelda Aygar

Department of Mathematics, Ankara University, 06100 Ankara, Turkey

Received 21 January 2011; Accepted 6 April 2011

Academic Editor: Svatoslav Staněk

Copyright © 2011 Murat Olgun et al. 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

We investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) 𝑎 𝑛 − 1 𝑦 𝑛 − 1 + 𝑏 𝑛 𝑦 𝑛 + 𝑎 𝑛 𝑦 𝑛 + 1 = 𝜆 𝑦 𝑛 , 𝑛 ∈ ℕ and ( 𝛾 0 + 𝛾 1 𝜆 ) 𝑦 1 + ( 𝛽 0 + 𝛽 1 𝜆 ) 𝑦 0 = 0 , where ( 𝑎 𝑛 ) and ( 𝑏 𝑛 ) are complex sequences, 𝜆 is an eigenparameter, and 𝛾 𝑖 , 𝛽 𝑖 ∈ ℂ for 𝑖 = 0 , 1.