descriptionPublicationkeyboard_double_arrow_right Article 09 Jul 2009 English Publisher:Springer Science and Business Media LLCJournal:Acta Applicandae Mathematicae, volume 111, pages 205-218 (issn: 0167-8019, eissn: 1572-9036,

Authors: José M. Rodríguez; Ana Portilla; Eva Tourís;

doi: 10.1007/s10440-009-9541-2

handle: 10016/6448

The Multiplication Operator, Zero Location and Asymptotic for Non-diagonal Sobolev Norms

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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 generalized non-diagonal Sobolev norm in which the product of the function and its derivative appears. 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.

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Keywords

Sobolev orthogonal polynomials, Matemáticas, Zero location, Multiplication operator, Asymptotic, Weighted Sobolev spaces, Weight, Extremal polynomials

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