An expansion for polynomials orthogonal over an analytic Jordan curve
| dc.creator | Miña-Díaz, Erwin | |
| dc.date | 2007-12-09 | |
| dc.date.accessioned | 2026-07-07T12:53:19Z | |
| dc.date.available | 2026-07-07T12:53:19Z | |
| dc.description | We consider polynomials that are orthogonal over an analytic Jordan curve L with respect to a positive analytic weight, and show that each such polynomial of sufficiently large degree can be expanded in a series of certain integral transforms that converges uniformly in the whole complex plane. This expansion yields, in particular and simultaneously, Szego's classical strong asymptotic formula and a new integral representation for the polynomials inside L. We further exploit such a representation to derive finer asymptotic results for weights having finitely many singularities (all of algebraic type) on a thin neighborhood of the orthogonality curve. Our results are a generalization of those previously obtained in [7] for the case of L being the unit circle. | |
| dc.description | 15 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0712.1366 | |
| dc.identifier | http://arxiv.org/abs/0712.1366 | |
| dc.identifier | Communications in Mathematical Physics. Vol. 285, 3:1109-1128 (2009) | |
| dc.identifier | doi:10.1007/s00220-008-0541-2 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223584 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 05E35 | |
| dc.title | An expansion for polynomials orthogonal over an analytic Jordan curve | |
| dc.type | text |