R II type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle
We consider a sequence of polynomials {P n } n≥0 satisfying a special R II type recurrence relation where the zeros of P n are simple and lie on the real line. It turns out that the polynomial P n , for any n≥2, is the characteristic polynomial of a simple n×n generalized eigenvalue problem. It is s...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2019 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositório: | Repositório Institucional da UNESP |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unesp.br:11449/188198 |
| Acesso em linha: | http://dx.doi.org/10.1016/j.laa.2018.10.005 http://hdl.handle.net/11449/188198 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Generalized eigenvalue problem Orthogonal polynomials on the unit circle |
| Resumo: | We consider a sequence of polynomials {P n } n≥0 satisfying a special R II type recurrence relation where the zeros of P n are simple and lie on the real line. It turns out that the polynomial P n , for any n≥2, is the characteristic polynomial of a simple n×n generalized eigenvalue problem. It is shown that with this R II type recurrence relation one can always associate a positive measure on the unit circle. The orthogonality property satisfied by P n with respect to this measure is also obtained. Finally, examples are given to justify the results. |
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