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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.09594 |
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| _version_ | 1866915666191187968 |
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| author | Ren, Guojing Xu, Guixin |
| author_facet | Ren, Guojing Xu, Guixin |
| contents | This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear relations of the non-self-adjoint systems are obtained. A bijective projection between all the quasi self-adjoint extensions of non-self-adjoint systems and all the self-adjoint extensions of the self-adjoint systems generated by the non-self-adjoint Hamiltonian systems is established in the general case. When the system is in the limit point case and $\I=[a,\infty)$, a complete characterization of all the quasi self-adjoint extensions is obtained by a subspace $Q\subset \C^{2n}$ with $\dim Q=n$ in terms of boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems Ren, Guojing Xu, Guixin Spectral Theory This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear relations of the non-self-adjoint systems are obtained. A bijective projection between all the quasi self-adjoint extensions of non-self-adjoint systems and all the self-adjoint extensions of the self-adjoint systems generated by the non-self-adjoint Hamiltonian systems is established in the general case. When the system is in the limit point case and $\I=[a,\infty)$, a complete characterization of all the quasi self-adjoint extensions is obtained by a subspace $Q\subset \C^{2n}$ with $\dim Q=n$ in terms of boundary conditions. |
| title | Quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2512.09594 |