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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 202851, 6 pages
http://dx.doi.org/10.1155/2013/202851
Research Article

Simplicity and Spectrum of Singular Hamiltonian Systems of Arbitrary Order

Department of Mathematics, Shandong University at Weihai, Weihai, Shandong 264209, China

Received 22 August 2013; Accepted 5 December 2013

Academic Editor: Douglas Anderson

Copyright © 2013 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.

Abstract

The paper is concerned with singular Hamiltonian systems of arbitrary order with arbitrary equal defect indices. It is proved that the minimal operator generated by the Hamiltonian system is simple. As a consequence, a sufficient condition is obtained for the continuous spectrum of every self-adjoint extension of the minimal operator to be empty in some interval and for the spectrum to be nowhere dense in this interval in terms of the numbers of linearly independent square integrable solutions.