On rational transformations of linear functionals: direct problem

13 pages, no figures.-- MSC2000 codes: 33C47, 42C05.MR#: MR2086540 (2005f:42051)Zbl#: Zbl 1066.33008Let u be a quasi-definite linear functional. We find necessary and sufficient conditions in order to the linear functional v satisfying $(x-\tilde{a})u=\lambda(x-a)v$ be a quasi-definite one. Also we analyze some linear relations linking the polynomials orthogonal with respect to u and v.M.A. and M.L.R. were partially supported by MCYT Grant BFM 2003-06335-C03-03 (Spain), FEDER funds (EU), and DGA E-12/25 (Spain). F.M. was partially supported by MCYT Grant BFM 2003-06335-C03-02 (Spain) and INTAS Research Network NeCCA INTAS 03-51-66378. A.P. was partially supported by MCYT Grant BFM 2001-1793 (Spain), FEDER funds (EU), and DGA E-12/25 (Spain).Publicad

Discrete Laguerre-Sobolev expansions: A Cohen type inequality

C. Markett proved a Cohen type inequality for the classical Laguerre expansions in the appropriate weighted $L^{p}$ spaces. In this paper, we get a Cohen type inequality for the Fourier expansions in terms of discrete Laguerre--Sobolev orthonormal polynomials with an arbitrary (finite) number of mass points. So, we extend the result due to B. Xh. Fejzullahu and F. Marcell\'an.Comment: Accepted in J. Math. Anal. App

Some properties of zeros of Sobolev-type orthogonal polynomials

9 pages, no figures.-- MSC1991 code: 33C45.MR#: MR1391618 (97f:33008)Zbl#: Zbl 0862.33005For polynomials orthogonal with respect to a discrete Sobolev product, we prove that, for each n, Qn has at least n − m zeros on the convex hull of the support of the measure, where m denotes the number of terms in the discrete part. Interlacing properties of zeros are also described.Research by first (M.A.) and third (M.L.R.) authors was partially supported by Diputación General de Aragón P CB-12/91 and by Comisión Interministerial de Ciencia y Tecnología (CICYT-Spain) PB93-0228-C02-02.Publicad