On the density of the minimal subspaces generated by discrete linear Hamiltonian systems |
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Affiliation: | School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, PR China |
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Abstract: | This paper focuses on the density of the minimal subspaces generated by a class of discrete linear Hamiltonian systems. It is shown that the minimal subspace is densely defined if and only if the maximal subspace is an operator; that is, it is single valued. In addition, it is shown that, if the interval on which the systems are defined is bounded from below or above, then the minimal subspace is non-densely defined in any non-trivial case. |
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Keywords: | Spectral theory Discrete linear Hamiltonian systems Minimal subspace Maximal subspace Density |
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