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Sobolev orthogonal polynomials with respect to measures supported on compact subsets of the complex plane are considered. For a wide class of such Sobolev orthogonal polynomials, it is proved that their zeros are contained in a compact subset of the complex plane and their asymptotic zero distribution is studied. We also find the nth root asymptotic… (More)

- Ulises Fidalgo Prieto, J. Illán, Guillermo López Lagomasino
- Journal of Approximation Theory
- 2004

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and… (More)

- Alexander I. Aptekarev, Valeriy A. Kalyagin, Guillermo López Lagomasino, I. A. Rocha
- Journal of Approximation Theory
- 2006

In this paper we investigate general properties of the coefficients in the recurrence relation satisfied by multiple orthogonal polynomials. The results include as particular cases Angelesco and Nikishin systems.

- Guillermo López Lagomasino, I. Pérez Izquierdo, H. Pijeira Cabrera
- Journal of Approximation Theory
- 2005

We study the zero location and asymptotic zero distribution of sequences of polynomials which satisfy an extremal condition with respect to a norm given on the space of all polynomials.

Using a nonlinear integral characterization of orthogonal polynomials in the complex plane, we provide a simple method for deducing a weak form of relative asymptotics exterior to the convex hull of the common support of the generating measures. The simplicity of the approach makes it a natural precursor for the presentation of Szegő theory. Dedicated to… (More)

- Dolores Barrios, Guillermo López Lagomasino, Edward B. Saff
- Journal of Approximation Theory
- 2003

Using a convergence theorem for Fourier-Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard’s theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szegő functions.

- Ulises Fidalgo Prieto, Guillermo López Lagomasino
- Journal of Approximation Theory
- 2011

- Dolores Barrios Rolanía, Guillermo López Lagomasino
- Adv. Comput. Math.
- 2007

We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic and their strong asymptotic under more restrictive conditions.

- Adhemar Bultheel, Guillermo López Lagomasino, Francisco Marcellán, Olav Njåstad, Ramón A. Orive Rodríguez
- J. Computational Applied Mathematics
- 2015

OrthoQuad 2014 was an international symposium on orthogonality, quadrature, and related topics, held on January 20-24, 2014 in Puerto de la Cruz, Tenerife, Spain. It was held in memory of Professor Pablo González-Vera (1955-2012). 1. A short CV of Pablo González-Vera Pablo González-Vera was born in Vallehermoso (La Gomera, Canary Islands) on January 25,… (More)

- Guillermo López Lagomasino, L. WUNDERLICH, Richard S. Varga
- 2008

Abstract. Many problems in science and engineering require the evaluation of functionals of the form Fu(A) = uT f(A)u, where A is a large symmetric matrix, u a vector, and f a nonlinear function. A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos… (More)