Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms

Authors:
Ana Portilla;Yamilet Quintana;José M. Rodríguez;Eva Tourís
Affiliations:
St. Louis University (Madrid Campus), Avenida del Valle 34, 28003 Madrid, Spain;Departamento de Matemáticas Puras y Aplicadas, Edificio Matemáticas y Sistemas (MYS), Apartado Postal: 89000, Caracas 1080 A, Universidad Simón Bolívar, Venezuela;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
Venue:
Journal of Approximation Theory
Year:
2010

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Abstract

In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a non-diagonal Sobolev norm in the worst case, i.e., when the quadratic form is allowed to degenerate. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. The multiplication operator by the independent variable is the main tool in order to obtain our results.