On the eigenvectors of the 5D discrete Fourier transform number operator in Newtonian basis
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910768857874432 |
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| author | Atakishiyev, Natig |
| author_facet | Atakishiyev, Natig |
| contents | A simple analytic approach to the evaluation of the eigenvalues and eigenvectors f_n of the 5D discrete number operator N_5 is formulated. This approach is essentially based on the symmetry of the intertwining operators with respect to the discrete reflection operator. A procedure for the sparsealization of the intertwining operators has been developed, which made it possible to establish a discrete analog of the well-known continuous case formula. A discrete analog for the eigenvectors f_n of another continuous case formula is constructed in the Newtonian basis polynomials, times the lowest eigenvector f_0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the eigenvectors of the 5D discrete Fourier transform number operator in Newtonian basis Atakishiyev, Natig Mathematical Physics Primary: 47A75, Secondaries: 11C20, 39A70, 39B42, 65T50 A simple analytic approach to the evaluation of the eigenvalues and eigenvectors f_n of the 5D discrete number operator N_5 is formulated. This approach is essentially based on the symmetry of the intertwining operators with respect to the discrete reflection operator. A procedure for the sparsealization of the intertwining operators has been developed, which made it possible to establish a discrete analog of the well-known continuous case formula. A discrete analog for the eigenvectors f_n of another continuous case formula is constructed in the Newtonian basis polynomials, times the lowest eigenvector f_0. |
| title | On the eigenvectors of the 5D discrete Fourier transform number operator in Newtonian basis |
| topic | Mathematical Physics Primary: 47A75, Secondaries: 11C20, 39A70, 39B42, 65T50 |
| url | https://arxiv.org/abs/2501.00148 |