Academic Editor: Alexander I. Domoshnitsky
Copyright © 2011 Bujar Xh. Fejzullahu and Francisco Marcellán. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let us introduce the Sobolev-type inner product , where and
and for all A Mehler-Heine-type formula and the inner strong asymptotics on
as well as some estimates for the polynomials orthogonal with respect to the above Sobolev inner product are obtained. Necessary conditions for the norm convergence of Fourier expansions in terms of such Sobolev orthogonal polynomials are given.