Mirror symmetric polynomials orthogonal on the unit circle
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912644076666880 |
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| author | Zhedanov, Alexei |
| author_facet | Zhedanov, Alexei |
| contents | We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric are presented. Corresponding unitary CMV matrices satisfy simple algebraic relations similar to relations for persymmetric tridiagonal matrices. We present three explicit examples of mirror symmetric OPUC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mirror symmetric polynomials orthogonal on the unit circle Zhedanov, Alexei Classical Analysis and ODEs Mathematical Physics 42C05, 47B36 We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric are presented. Corresponding unitary CMV matrices satisfy simple algebraic relations similar to relations for persymmetric tridiagonal matrices. We present three explicit examples of mirror symmetric OPUC. |
| title | Mirror symmetric polynomials orthogonal on the unit circle |
| topic | Classical Analysis and ODEs Mathematical Physics 42C05, 47B36 |
| url | https://arxiv.org/abs/2510.10447 |