Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509688 | Journal of Computational and Applied Mathematics | 2005 | 19 Pages |
Abstract
Let μ be a finite positive Borel measure supported on a compact set of the real line and introduce the discrete Sobolev-type inner productãf,gã=â«f(x)g(x)dμ(x)+âk=1Kâi=0NkMk,if(i)(ck)g(i)(ck),where the mass points ck belong to supp(μ) and Mk,i are complex numbers such that Mk,Nkâ 0. In this paper we investigate the asymptotics of the polynomials orthogonal with this product. When the mass points ck belong to C⧹supp(μ), the problem was solved in a paper by G. López, et al. (Constr. Approx. 11 (1995) 107-137) and, for mass points in supp(μ)=[-1,1], the solution was given by I.A. Rocha et al. (J. Approx. Theory, 121 (2003) 336-356) provided that μâ²(x)>0 a.e. xâ[-1,1] and Mk,i are nonnegative constants. If μâM(0,1), the possibility ckâsupp(μ)⧹[-1,1] must be considered. Here we solve this last case with complex constants Mk,i.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
I. Alvarez Rocha, L. Salto,