Bounds on Tur{á}n determinants
| dc.creator | Berg, Christian | |
| dc.creator | Szwarc, Ryszard | |
| dc.date | 2007-12-10 | |
| dc.date.accessioned | 2026-07-07T08:48:16Z | |
| dc.date.available | 2026-07-07T08:48:16Z | |
| dc.description | Let μdenote a symmetric probability measure on [-1,1] and let (p_n) be the corresponding orthogonal polynomials normalized such that p_n(1)=1. We prove that the normalized Tur{á}n determinant Δ_n(x)/(1-x^2), where Δ_n=p_n^2-p_{n-1}p_{n+1}, is a Tur{á}n determinant of order n-1 for orthogonal polynomials with respect to (1-x^2)dμ(x). We use this to prove lower and upper bounds for the normalized Tur{á}n determinant in the interval -1<x<1. | |
| dc.identifier | https://arxiv.org/abs/0712.1460 | |
| dc.identifier | http://arxiv.org/abs/0712.1460 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143886 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33C45;26D07 | |
| dc.title | Bounds on Tur{á}n determinants | |
| dc.type | text |