Sobolev orthogonal polynomials: balance and asymptotics
| dc.creator | Alfaro, M. | |
| dc.creator | Moreno-Balcazar, J. J. | |
| dc.creator | Pena, A. | |
| dc.creator | Rezola, M. L. | |
| dc.date | 2006-06-23 | |
| dc.date | 2007-05-02 | |
| dc.date.accessioned | 2026-07-07T07:59:00Z | |
| dc.date.available | 2026-07-07T07:59:00Z | |
| dc.description | Let $μ_0$ and $μ_1$ be measures supported on an unbounded interval and $S_{n,λ_n}$ the extremal varying Sobolev polynomial which minimizes \begin{equation*} < P, P >_{λ_n}=\int P^2 dμ_0 + λ_n \int P'^2 dμ_1, \quad λ_n >0 \end{equation*} \noindent in the class of all monic polynomials of degree $n$. The goal of this paper is twofold. On one hand, we discuss how to balance both terms of this inner product, that is, how to choose a sequence $(λ_n)$ such that both measures $μ_0$ and $μ_1$ play a role in the asymptotics of $(S_{n, λ_n}).$ On the other, we apply such ideas to the case when both $μ_0$ and $μ_1$ are Freud weights. Asymptotics for the corresponding $S_{n, λ_n}$ are computed, illustrating the accuracy of the choice of $λ_n .$ | |
| dc.description | 20 pages. Changed content | |
| dc.identifier | https://arxiv.org/abs/math/0606589 | |
| dc.identifier | http://arxiv.org/abs/math/0606589 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128209 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42C05 | |
| dc.title | Sobolev orthogonal polynomials: balance and asymptotics | |
| dc.type | text |