Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912781639352320 |
|---|---|
| author | Kozhan, Rostyslav Štampach, František |
| author_facet | Kozhan, Rostyslav Štampach, František |
| contents | We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients $α_{n,N}$ when the ratio $n/N$ converges as $n,N\to\infty$.
First, we give a streamlined proof of ratio asymptotics for orthogonal and paraorthogonal polynomials in the case of asymptotically constant and asymptotically periodic coefficients $α_{n,N}$.
Second, we determine the asymptotic zero distribution of paraorthogonal polynomials in the locally constant and locally periodic regimes. Analogous results are obtained for orthogonal polynomials under a mild additional condition on the varying coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients Kozhan, Rostyslav Štampach, František Classical Analysis and ODEs Mathematical Physics Spectral Theory 42C05, 30C15 We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients $α_{n,N}$ when the ratio $n/N$ converges as $n,N\to\infty$. First, we give a streamlined proof of ratio asymptotics for orthogonal and paraorthogonal polynomials in the case of asymptotically constant and asymptotically periodic coefficients $α_{n,N}$. Second, we determine the asymptotic zero distribution of paraorthogonal polynomials in the locally constant and locally periodic regimes. Analogous results are obtained for orthogonal polynomials under a mild additional condition on the varying coefficients. |
| title | Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients |
| topic | Classical Analysis and ODEs Mathematical Physics Spectral Theory 42C05, 30C15 |
| url | https://arxiv.org/abs/2511.22507 |