Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914306912681984 |
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| author | Świderski, Grzegorz Trojan, Bartosz |
| author_facet | Świderski, Grzegorz Trojan, Bartosz |
| contents | We study spectrum of finite truncations of unbounded Jacobi matrices with periodically modulated entries. In particular, we show that under some hypotheses a sequence of properly normalized eigenvalue counting measures converge vaguely to an explicit infinite Radon measure. To do so we link the asymptotic behavior of the Christoffel-Darboux kernel on the diagonal with the limiting measure. Finally, we derive strong asymptotics of the associated orthogonal polynomials in the complex plane, which allows us to prove that Cauchy transforms of the normalized eigenvalue counting measures converge pointwise and which leads to a stronger notion of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04853 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients Świderski, Grzegorz Trojan, Bartosz Spectral Theory Mathematical Physics Classical Analysis and ODEs 42C05 (Primary) 47B36 (Secondary) We study spectrum of finite truncations of unbounded Jacobi matrices with periodically modulated entries. In particular, we show that under some hypotheses a sequence of properly normalized eigenvalue counting measures converge vaguely to an explicit infinite Radon measure. To do so we link the asymptotic behavior of the Christoffel-Darboux kernel on the diagonal with the limiting measure. Finally, we derive strong asymptotics of the associated orthogonal polynomials in the complex plane, which allows us to prove that Cauchy transforms of the normalized eigenvalue counting measures converge pointwise and which leads to a stronger notion of convergence. |
| title | Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients |
| topic | Spectral Theory Mathematical Physics Classical Analysis and ODEs 42C05 (Primary) 47B36 (Secondary) |
| url | https://arxiv.org/abs/2311.04853 |