Periodic approximations in inverse spectral problems for canonical Hamiltonian systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916357514199040 |
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| author | Poltoratski, Alexei Zhang, Ashley Ran |
| author_facet | Poltoratski, Alexei Zhang, Ashley Ran |
| contents | This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when the spectral measure of the system is a locally finite periodic measure (see \cite{MP}). In this note we extend the periodic algorithm to the case of non-periodic measures by considering periodizations of a spectral measure and showing that the Hamiltonians corresponding to the periodizations converge to the Hamiltonian of the original measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00055 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Periodic approximations in inverse spectral problems for canonical Hamiltonian systems Poltoratski, Alexei Zhang, Ashley Ran Spectral Theory This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when the spectral measure of the system is a locally finite periodic measure (see \cite{MP}). In this note we extend the periodic algorithm to the case of non-periodic measures by considering periodizations of a spectral measure and showing that the Hamiltonians corresponding to the periodizations converge to the Hamiltonian of the original measure. |
| title | Periodic approximations in inverse spectral problems for canonical Hamiltonian systems |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2208.00055 |