Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913337956106240 |
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| author | Vaktnäs, Marcus Kozhan, Rostyslav |
| author_facet | Vaktnäs, Marcus Kozhan, Rostyslav |
| contents | We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel$\unicode{x2013}$Darboux formula. These results stand directly in analogue with the nearest neighbour recurrence relations from the real line counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle Vaktnäs, Marcus Kozhan, Rostyslav Classical Analysis and ODEs Spectral Theory 42C05, 47B36, 41A21 We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel$\unicode{x2013}$Darboux formula. These results stand directly in analogue with the nearest neighbour recurrence relations from the real line counterpart. |
| title | Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle |
| topic | Classical Analysis and ODEs Spectral Theory 42C05, 47B36, 41A21 |
| url | https://arxiv.org/abs/2404.18666 |