Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899322 | Journal of Mathematical Analysis and Applications | 2018 | 24 Pages |
Abstract
In this paper we will discuss asymptotic properties of monic polynomials {Snλ(x)}nâ¥0 orthogonal with respect to the Sobolev inner productãp,qãS=â«Rp(x)q(x)dμ0+λâ«Rpâ²(x)qâ²(x)dμ1, with λ>0, dμ0=eâx2dx, dμ1=x2+ax2+beâx2dx, a,bâR+ and aâ b. It is well known that (μ0,μ1) is a pair of symmetric (1,1)-coherent measures. This means that there exist sequences {an}nâN, {bn}nâN, anâ bn for every nâN, such that the algebraic relationHn(x)+bnâ2Hnâ2(x)=Qn(x)+anâ2Qnâ2(x),nâ¥2, is satisfied, where {Qn(x)}nâ¥0 is the sequence of monic orthogonal polynomials associated with μ1 and {Hn(x)}nâ¥0 is the sequence of monic Hermite polynomials. We will study the relative asymptotics for Sobolev scaled polynomials and we will obtain Mehler-Heine type formulas, among others.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Herbert Dueñas Ruiz, Francisco Marcellán Español, Alejandro Molano Molano,