Meromorphic Szego functions and asymptotic series for Verblunsky coefficients
| dc.creator | Simon, Barry | |
| dc.date | 2005-02-23 | |
| dc.date.accessioned | 2026-07-07T05:17:25Z | |
| dc.date.available | 2026-07-07T05:17:25Z | |
| dc.description | We prove that the Szegő function, $D(z)$, of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponentials. We relate the positions of the poles of $D(z)^{-1}$ to the exponential rates in the asymptotic expansion. Basically, either set is contained in the sets generated from the other by considering products of the form, $z_1 ... z_\ell \bar z_{\ell-1}... \bar z_{2\ell-1}$ with $z_j$ in the set. The proofs use nothing more than iterated Szegő recursion at $z$ and $1/\bar z$. | |
| dc.identifier | https://arxiv.org/abs/math/0502489 | |
| dc.identifier | http://arxiv.org/abs/math/0502489 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74293 | |
| dc.subject | Spectral Theory | |
| dc.subject | 42C05; 30D30 | |
| dc.title | Meromorphic Szego functions and asymptotic series for Verblunsky coefficients | |
| dc.type | text |