Essential spectrum of singular discrete linear Hamiltonian systems |
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Authors: | Huaqing Sun Qingkai Kong Yuming Shi |
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Affiliation: | 1. Department of Mathematics, Shandong University, Jinan, P. R. China;2. Department of Mathematics, Shandong University, Weihai, P. R. China;3. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, USA |
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Abstract: | The paper is concerned with the essential spectral points of singular discrete linear Hamiltonian systems. Several sufficient conditions for a real point to be in the essential spectrum are obtained in terms of the number of linearly independent square‐summable solutions of the corresponding homogeneous linear system, and a sufficient and necessary condition for a real point to be in the essential spectrum is given in terms of the number of linearly independent square‐summable solutions of the corresponding nonhomogeneous linear system. As a direct consequence, the corresponding results for singular higher‐order symmetric vector difference expressions are given. |
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Keywords: | Singular discrete linear Hamiltonian system essential spectrum defect index Primary: 34B20 34L05 Secondary: 47E05 |
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