Seminario Grupo de Teoría de Aproximación y Polinomios Ortogonales

El Grupo de Teoría de Aproximación y Polinomios Ortogonales organiza el Seminario cuyos datos se detallan a continuación:
Fecha: Viernes, 29 de noviembre de 2013
Lugar: Seminario 1ª Planta, Instituto de Matemáticas IEMath-GR, Uiversidad de Granada

Sesión 11:30. Yuan Xu (University of Oregon)
Título: Approximation and Sobolev Orthogonal Polynomials on Unit Ball
Abstract: For the spectral Galerkin method in numerical solution of partial differential equations, we need to understand the approximation by polynomials in the Sobolev spaces. For this purpose, it is necessary to study orthogonal structure of the Sobolev space $W_2^r$ that consists of functions whose derivatives up to $r$-th order are all in $L^2$. In this talk, we discuss new result on Sobolev orthogonal polynomials in $W_2^r$ for all positive integer $r$ and approximation in the Sobolev space on the unit ball in $\mathbb{R}^d$, and describe sharp estimate for the error of best approximation in the Sobolev space and its application in the spectral Galerkin methods.

Sesión 12:45. Andrei Martínez Finkelshtein (Universidad de Almería)
Title: Equilibrium problems related to asymptotics of Hermite-Padé polynomials.
Abstract: Polynomials of multiple orthogonality (or Hermite-Padé polynomials) arise in many problems related to number theory, random matrix theory and stochastic processes, to mention a few. It became clear recently that understanding their asymptotic is crucial for solving many open problems in these areas. It is well-known that the logarithmic potential and in particular, equilibrium measures, provide the description of the leading term of asymptotics for standard orthogonal polynomials. However, the situation is much more difficult and less clear for the Hermite-Padé polynomials, where the general theory is still to be created. I will explain some ideas about the vector equilibrium for these polynomials, based on the work of Gonchar, Rakhmanov, Aptekarev and others.

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