A Sharp Inequality of Markov Type for Polynomials Associated with Laguerre Weight

AbstractThe best possible constant An in an inequality of Markov type [ddx(e−xpn(x))][0, ∞)⩽An‖e−xpn(x)‖[0, ∞), where ‖·‖[0, ∞) denotes the sup-norm on the half real line [0, ∞) and pn is an arbitrary polynomial of degree at most n, is determined in terms of the weighted Chebyshev polynomials associated with the Laguerre weight e−x on [0, ∞)

Weighted Sobolev spaces: Markov-type inequalities and duality

Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. The aim of this paper is to prove several important properties of weighted Sobolev spaces: separability, reflexivity, uniform convexity, duality and Markov-type inequalities.Francisco Marcellán: Supported in part by two Grants from Ministerio de Economía y Competitividad (MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P), Spain. Yamilet Quintana: Supported in part by a Grant from Ministerio de Economía y Competitividad (MTM2012-36732-C03-01), Spain. José M. Rodríguez: Supported in part by three Grants from Ministerio de Economía y Competititvidad, Agencia Estatal de Investigacin (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2013-46374-P, MTM2016-78227-C2-1-P and MTM2015-69323-REDT), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials