The Glazman--Krein--Naimark theory for a class of discrete Hamiltonian systems (Q860672)
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scientific article; zbMATH DE number 5083357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Glazman--Krein--Naimark theory for a class of discrete Hamiltonian systems |
scientific article; zbMATH DE number 5083357 |
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The Glazman--Krein--Naimark theory for a class of discrete Hamiltonian systems (English)
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9 January 2007
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The authors study the Glazman-Krein-Naimark (GKN) theory for a class of discrete Hamiltonian systems. A minimal and maximal operators, GKN-sets, and a boundary space for the system are introduced. Algebraic characterizations of the domains of self-adjoint extensions of the minimal operator are given. A close relationship between the domains self-adjoint extensions and the GKN-sets is established. It is shown that there exist one-to-one correspondences among the set of all the self-adjoint extensions, the set of all the \(d\)-dimensional Lagrangian subspaces of the boundary space, and the set of all the complete Lagrangian subspaces of the boundary space.
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discrete Hamiltonian system
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Glazman-Krein-Naimark theory
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complex symplectic geometry
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self-adjoint extension
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Lagrangian subspace
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