The Szego class with a polynomial weight
| dc.creator | Denisov, S. | |
| dc.creator | Kupin, S. | |
| dc.date | 2004-03-26 | |
| dc.date.accessioned | 2026-07-07T05:06:48Z | |
| dc.date.available | 2026-07-07T05:06:48Z | |
| dc.description | Let p be a trigonometric polynomial, nonnegative on the unit circle $\mathbb{T}$. We say that a measure $σ$ on $\mathbb{T}$ belongs to the polynomial Szego class, if $dσ=sigma'_{ac}dθ+dσ_s$, $σ_s$ is singular, and $p\ln σ'_{ac}$ is summable on $\mathbb{T}$. For the associated orthogonal polynomials, we obtain pointwise asymptotics inside the unit disc. Then, we show that this asymptotics holds in the $L^2$ sense on the unit circle. As a corollary, we get existense of certain modified wave operators. | |
| dc.description | preliminary version | |
| dc.identifier | https://arxiv.org/abs/math/0403472 | |
| dc.identifier | http://arxiv.org/abs/math/0403472 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70617 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 47B36, 42C05 | |
| dc.title | The Szego class with a polynomial weight | |
| dc.type | text |