Ruijsenaars spectral transform
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909624351850496 |
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| author | Belousov, N. Khoroshkin, S. |
| author_facet | Belousov, N. Khoroshkin, S. |
| contents | Spectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of analytical symmetric functions we prove inversion formula and orthogonality relations, valid for complex valued parameters of the system. Besides, we study four regimes of unitarity, when this transform defines isomorphisms of the corresponding $L_2$ spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ruijsenaars spectral transform Belousov, N. Khoroshkin, S. Mathematical Physics High Energy Physics - Theory Classical Analysis and ODEs Exactly Solvable and Integrable Systems Spectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of analytical symmetric functions we prove inversion formula and orthogonality relations, valid for complex valued parameters of the system. Besides, we study four regimes of unitarity, when this transform defines isomorphisms of the corresponding $L_2$ spaces. |
| title | Ruijsenaars spectral transform |
| topic | Mathematical Physics High Energy Physics - Theory Classical Analysis and ODEs Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.19659 |