Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 904976, 19 pages
Research Article

-Self-Adjoint Extensions for a Class of Discrete Linear Hamiltonian Systems

1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, China
2Department of Mathematics, Shandong University at Weihai, Weihai, Shandong 264209, China

Received 15 January 2013; Accepted 18 March 2013

Academic Editor: Michiel Bertsch

Copyright © 2013 Guojing Ren and Huaqing Sun. 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.


This paper is concerned with formally -self-adjoint discrete linear Hamiltonian systems on finite or infinite intervals. The minimal and maximal subspaces are characterized, and the defect indices of the minimal subspaces are discussed. All the -self-adjoint subspace extensions of the minimal subspace are completely characterized in terms of the square summable solutions and boundary conditions. As a consequence, characterizations of all the -self-adjoint subspace extensions are given in the limit point and limit circle cases.