Etudes in the inverse spectral problem, II
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912585462317056 |
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| author | Makarov, Nikolai Poltoratski, Alexei |
| author_facet | Makarov, Nikolai Poltoratski, Alexei |
| contents | We apply the approach developed in our previous papers to obtain examples of solutions to the inverse spectral problem (ISP) for the canonical Hamiltonian system. One of our goals is to illustrate connections of ISP with classical tools of analysis, such as the Hilbert transform and solutions to the Riemann-Hilbert problem. A key role in our study is played by the systems with homogeneous and quasi-homogeneous spectral measures. We show how some of such systems give rise to families of Bessel functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Etudes in the inverse spectral problem, II Makarov, Nikolai Poltoratski, Alexei Complex Variables 39, 30 We apply the approach developed in our previous papers to obtain examples of solutions to the inverse spectral problem (ISP) for the canonical Hamiltonian system. One of our goals is to illustrate connections of ISP with classical tools of analysis, such as the Hilbert transform and solutions to the Riemann-Hilbert problem. A key role in our study is played by the systems with homogeneous and quasi-homogeneous spectral measures. We show how some of such systems give rise to families of Bessel functions. |
| title | Etudes in the inverse spectral problem, II |
| topic | Complex Variables 39, 30 |
| url | https://arxiv.org/abs/2509.10699 |